On Rereading Stein’s Lemma: Its Intrinsic Connection with Cramér-Rao Identity and Some New Identities
Abstract Now is an opportune time to revisit Stein’s (1973) beautiful lemma all over again. It is especially so since researchers have recently begun discovering a great deal of potential of closely related Stein’s unbiased risk estimate (SURE) in a number of directions involving novel applications....
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| Autor*in: |
Mukhopadhyay, Nitis [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2020 |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: Methodology and computing in applied probability - Dordrecht [u.a.] : Springer Science + Business Media B.V, 1999, 23(2020), 1 vom: 31. Okt., Seite 355-367 |
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| Übergeordnetes Werk: |
volume:23 ; year:2020 ; number:1 ; day:31 ; month:10 ; pages:355-367 |
| Links: |
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| DOI / URN: |
10.1007/s11009-020-09830-w |
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SPR043392482 |
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| 520 | |a Abstract Now is an opportune time to revisit Stein’s (1973) beautiful lemma all over again. It is especially so since researchers have recently begun discovering a great deal of potential of closely related Stein’s unbiased risk estimate (SURE) in a number of directions involving novel applications. In recognition of the importance of the topic of Stein’s (1973; Ann Statist 9:1135–1151, 1981) research and its elegance, we include a selective review from the field. The process of rereading Stein’s lemma and reliving its awesome simplicity as well as versatility rekindled a number of personal thoughts, queries, and observations. A number of new and interesting insights are highlighted in the spirit of providing updated and futuristic versions of the celebrated lemma by largely focusing on univariate continuous distributions not belonging to an exponential family. In doing so, a number of new identities have emerged when the parent population is continuous, but they are highly non-normal. Last, but not the least, we have argued that there is no big foundational difference between the basic messages obtained via Stein’s identity and Cramér-Rao identity. | ||
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| 650 | 4 | |a Cramér-Rao identity |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Exponential family |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Identities |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Non-exponential family |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Non-normal distributions |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Poisson approximation |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Shrinkage estimation |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Stein identity |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a SURE |7 (dpeaa)DE-He213 | |
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10.1007/s11009-020-09830-w doi (DE-627)SPR043392482 (DE-599)SPRs11009-020-09830-w-e (SPR)s11009-020-09830-w-e DE-627 ger DE-627 rakwb eng 004 ASE 31.70 bkl 31.80 bkl Mukhopadhyay, Nitis verfasserin aut On Rereading Stein’s Lemma: Its Intrinsic Connection with Cramér-Rao Identity and Some New Identities 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Now is an opportune time to revisit Stein’s (1973) beautiful lemma all over again. It is especially so since researchers have recently begun discovering a great deal of potential of closely related Stein’s unbiased risk estimate (SURE) in a number of directions involving novel applications. In recognition of the importance of the topic of Stein’s (1973; Ann Statist 9:1135–1151, 1981) research and its elegance, we include a selective review from the field. The process of rereading Stein’s lemma and reliving its awesome simplicity as well as versatility rekindled a number of personal thoughts, queries, and observations. A number of new and interesting insights are highlighted in the spirit of providing updated and futuristic versions of the celebrated lemma by largely focusing on univariate continuous distributions not belonging to an exponential family. In doing so, a number of new identities have emerged when the parent population is continuous, but they are highly non-normal. Last, but not the least, we have argued that there is no big foundational difference between the basic messages obtained via Stein’s identity and Cramér-Rao identity. Chen-Stein approximation (dpeaa)DE-He213 Continuous distributions (dpeaa)DE-He213 Cramér-Rao identity (dpeaa)DE-He213 Exponential family (dpeaa)DE-He213 Identities (dpeaa)DE-He213 Non-exponential family (dpeaa)DE-He213 Non-normal distributions (dpeaa)DE-He213 Poisson approximation (dpeaa)DE-He213 Shrinkage estimation (dpeaa)DE-He213 Stein identity (dpeaa)DE-He213 SURE (dpeaa)DE-He213 Enthalten in Methodology and computing in applied probability Dordrecht [u.a.] : Springer Science + Business Media B.V, 1999 23(2020), 1 vom: 31. Okt., Seite 355-367 (DE-627)320427412 (DE-600)2003336-9 1573-7713 nnns volume:23 year:2020 number:1 day:31 month:10 pages:355-367 https://dx.doi.org/10.1007/s11009-020-09830-w lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.70 ASE 31.80 ASE AR 23 2020 1 31 10 355-367 |
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10.1007/s11009-020-09830-w doi (DE-627)SPR043392482 (DE-599)SPRs11009-020-09830-w-e (SPR)s11009-020-09830-w-e DE-627 ger DE-627 rakwb eng 004 ASE 31.70 bkl 31.80 bkl Mukhopadhyay, Nitis verfasserin aut On Rereading Stein’s Lemma: Its Intrinsic Connection with Cramér-Rao Identity and Some New Identities 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Now is an opportune time to revisit Stein’s (1973) beautiful lemma all over again. It is especially so since researchers have recently begun discovering a great deal of potential of closely related Stein’s unbiased risk estimate (SURE) in a number of directions involving novel applications. In recognition of the importance of the topic of Stein’s (1973; Ann Statist 9:1135–1151, 1981) research and its elegance, we include a selective review from the field. The process of rereading Stein’s lemma and reliving its awesome simplicity as well as versatility rekindled a number of personal thoughts, queries, and observations. A number of new and interesting insights are highlighted in the spirit of providing updated and futuristic versions of the celebrated lemma by largely focusing on univariate continuous distributions not belonging to an exponential family. In doing so, a number of new identities have emerged when the parent population is continuous, but they are highly non-normal. Last, but not the least, we have argued that there is no big foundational difference between the basic messages obtained via Stein’s identity and Cramér-Rao identity. Chen-Stein approximation (dpeaa)DE-He213 Continuous distributions (dpeaa)DE-He213 Cramér-Rao identity (dpeaa)DE-He213 Exponential family (dpeaa)DE-He213 Identities (dpeaa)DE-He213 Non-exponential family (dpeaa)DE-He213 Non-normal distributions (dpeaa)DE-He213 Poisson approximation (dpeaa)DE-He213 Shrinkage estimation (dpeaa)DE-He213 Stein identity (dpeaa)DE-He213 SURE (dpeaa)DE-He213 Enthalten in Methodology and computing in applied probability Dordrecht [u.a.] : Springer Science + Business Media B.V, 1999 23(2020), 1 vom: 31. Okt., Seite 355-367 (DE-627)320427412 (DE-600)2003336-9 1573-7713 nnns volume:23 year:2020 number:1 day:31 month:10 pages:355-367 https://dx.doi.org/10.1007/s11009-020-09830-w lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.70 ASE 31.80 ASE AR 23 2020 1 31 10 355-367 |
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10.1007/s11009-020-09830-w doi (DE-627)SPR043392482 (DE-599)SPRs11009-020-09830-w-e (SPR)s11009-020-09830-w-e DE-627 ger DE-627 rakwb eng 004 ASE 31.70 bkl 31.80 bkl Mukhopadhyay, Nitis verfasserin aut On Rereading Stein’s Lemma: Its Intrinsic Connection with Cramér-Rao Identity and Some New Identities 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Now is an opportune time to revisit Stein’s (1973) beautiful lemma all over again. It is especially so since researchers have recently begun discovering a great deal of potential of closely related Stein’s unbiased risk estimate (SURE) in a number of directions involving novel applications. In recognition of the importance of the topic of Stein’s (1973; Ann Statist 9:1135–1151, 1981) research and its elegance, we include a selective review from the field. The process of rereading Stein’s lemma and reliving its awesome simplicity as well as versatility rekindled a number of personal thoughts, queries, and observations. A number of new and interesting insights are highlighted in the spirit of providing updated and futuristic versions of the celebrated lemma by largely focusing on univariate continuous distributions not belonging to an exponential family. In doing so, a number of new identities have emerged when the parent population is continuous, but they are highly non-normal. Last, but not the least, we have argued that there is no big foundational difference between the basic messages obtained via Stein’s identity and Cramér-Rao identity. Chen-Stein approximation (dpeaa)DE-He213 Continuous distributions (dpeaa)DE-He213 Cramér-Rao identity (dpeaa)DE-He213 Exponential family (dpeaa)DE-He213 Identities (dpeaa)DE-He213 Non-exponential family (dpeaa)DE-He213 Non-normal distributions (dpeaa)DE-He213 Poisson approximation (dpeaa)DE-He213 Shrinkage estimation (dpeaa)DE-He213 Stein identity (dpeaa)DE-He213 SURE (dpeaa)DE-He213 Enthalten in Methodology and computing in applied probability Dordrecht [u.a.] : Springer Science + Business Media B.V, 1999 23(2020), 1 vom: 31. Okt., Seite 355-367 (DE-627)320427412 (DE-600)2003336-9 1573-7713 nnns volume:23 year:2020 number:1 day:31 month:10 pages:355-367 https://dx.doi.org/10.1007/s11009-020-09830-w lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.70 ASE 31.80 ASE AR 23 2020 1 31 10 355-367 |
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10.1007/s11009-020-09830-w doi (DE-627)SPR043392482 (DE-599)SPRs11009-020-09830-w-e (SPR)s11009-020-09830-w-e DE-627 ger DE-627 rakwb eng 004 ASE 31.70 bkl 31.80 bkl Mukhopadhyay, Nitis verfasserin aut On Rereading Stein’s Lemma: Its Intrinsic Connection with Cramér-Rao Identity and Some New Identities 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Now is an opportune time to revisit Stein’s (1973) beautiful lemma all over again. It is especially so since researchers have recently begun discovering a great deal of potential of closely related Stein’s unbiased risk estimate (SURE) in a number of directions involving novel applications. In recognition of the importance of the topic of Stein’s (1973; Ann Statist 9:1135–1151, 1981) research and its elegance, we include a selective review from the field. The process of rereading Stein’s lemma and reliving its awesome simplicity as well as versatility rekindled a number of personal thoughts, queries, and observations. A number of new and interesting insights are highlighted in the spirit of providing updated and futuristic versions of the celebrated lemma by largely focusing on univariate continuous distributions not belonging to an exponential family. In doing so, a number of new identities have emerged when the parent population is continuous, but they are highly non-normal. Last, but not the least, we have argued that there is no big foundational difference between the basic messages obtained via Stein’s identity and Cramér-Rao identity. Chen-Stein approximation (dpeaa)DE-He213 Continuous distributions (dpeaa)DE-He213 Cramér-Rao identity (dpeaa)DE-He213 Exponential family (dpeaa)DE-He213 Identities (dpeaa)DE-He213 Non-exponential family (dpeaa)DE-He213 Non-normal distributions (dpeaa)DE-He213 Poisson approximation (dpeaa)DE-He213 Shrinkage estimation (dpeaa)DE-He213 Stein identity (dpeaa)DE-He213 SURE (dpeaa)DE-He213 Enthalten in Methodology and computing in applied probability Dordrecht [u.a.] : Springer Science + Business Media B.V, 1999 23(2020), 1 vom: 31. Okt., Seite 355-367 (DE-627)320427412 (DE-600)2003336-9 1573-7713 nnns volume:23 year:2020 number:1 day:31 month:10 pages:355-367 https://dx.doi.org/10.1007/s11009-020-09830-w lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.70 ASE 31.80 ASE AR 23 2020 1 31 10 355-367 |
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10.1007/s11009-020-09830-w doi (DE-627)SPR043392482 (DE-599)SPRs11009-020-09830-w-e (SPR)s11009-020-09830-w-e DE-627 ger DE-627 rakwb eng 004 ASE 31.70 bkl 31.80 bkl Mukhopadhyay, Nitis verfasserin aut On Rereading Stein’s Lemma: Its Intrinsic Connection with Cramér-Rao Identity and Some New Identities 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Now is an opportune time to revisit Stein’s (1973) beautiful lemma all over again. It is especially so since researchers have recently begun discovering a great deal of potential of closely related Stein’s unbiased risk estimate (SURE) in a number of directions involving novel applications. In recognition of the importance of the topic of Stein’s (1973; Ann Statist 9:1135–1151, 1981) research and its elegance, we include a selective review from the field. The process of rereading Stein’s lemma and reliving its awesome simplicity as well as versatility rekindled a number of personal thoughts, queries, and observations. A number of new and interesting insights are highlighted in the spirit of providing updated and futuristic versions of the celebrated lemma by largely focusing on univariate continuous distributions not belonging to an exponential family. In doing so, a number of new identities have emerged when the parent population is continuous, but they are highly non-normal. Last, but not the least, we have argued that there is no big foundational difference between the basic messages obtained via Stein’s identity and Cramér-Rao identity. Chen-Stein approximation (dpeaa)DE-He213 Continuous distributions (dpeaa)DE-He213 Cramér-Rao identity (dpeaa)DE-He213 Exponential family (dpeaa)DE-He213 Identities (dpeaa)DE-He213 Non-exponential family (dpeaa)DE-He213 Non-normal distributions (dpeaa)DE-He213 Poisson approximation (dpeaa)DE-He213 Shrinkage estimation (dpeaa)DE-He213 Stein identity (dpeaa)DE-He213 SURE (dpeaa)DE-He213 Enthalten in Methodology and computing in applied probability Dordrecht [u.a.] : Springer Science + Business Media B.V, 1999 23(2020), 1 vom: 31. Okt., Seite 355-367 (DE-627)320427412 (DE-600)2003336-9 1573-7713 nnns volume:23 year:2020 number:1 day:31 month:10 pages:355-367 https://dx.doi.org/10.1007/s11009-020-09830-w lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.70 ASE 31.80 ASE AR 23 2020 1 31 10 355-367 |
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It is especially so since researchers have recently begun discovering a great deal of potential of closely related Stein’s unbiased risk estimate (SURE) in a number of directions involving novel applications. In recognition of the importance of the topic of Stein’s (1973; Ann Statist 9:1135–1151, 1981) research and its elegance, we include a selective review from the field. The process of rereading Stein’s lemma and reliving its awesome simplicity as well as versatility rekindled a number of personal thoughts, queries, and observations. A number of new and interesting insights are highlighted in the spirit of providing updated and futuristic versions of the celebrated lemma by largely focusing on univariate continuous distributions not belonging to an exponential family. In doing so, a number of new identities have emerged when the parent population is continuous, but they are highly non-normal. Last, but not the least, we have argued that there is no big foundational difference between the basic messages obtained via Stein’s identity and Cramér-Rao identity.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Chen-Stein approximation</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Continuous distributions</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Cramér-Rao identity</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Exponential family</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Identities</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Non-exponential family</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Non-normal distributions</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Poisson approximation</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Shrinkage estimation</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Stein identity</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">SURE</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Methodology and computing in applied probability</subfield><subfield code="d">Dordrecht [u.a.] : Springer Science + Business Media B.V, 1999</subfield><subfield code="g">23(2020), 1 vom: 31. 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Mukhopadhyay, Nitis |
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Mukhopadhyay, Nitis ddc 004 bkl 31.70 bkl 31.80 misc Chen-Stein approximation misc Continuous distributions misc Cramér-Rao identity misc Exponential family misc Identities misc Non-exponential family misc Non-normal distributions misc Poisson approximation misc Shrinkage estimation misc Stein identity misc SURE On Rereading Stein’s Lemma: Its Intrinsic Connection with Cramér-Rao Identity and Some New Identities |
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004 ASE 31.70 bkl 31.80 bkl On Rereading Stein’s Lemma: Its Intrinsic Connection with Cramér-Rao Identity and Some New Identities Chen-Stein approximation (dpeaa)DE-He213 Continuous distributions (dpeaa)DE-He213 Cramér-Rao identity (dpeaa)DE-He213 Exponential family (dpeaa)DE-He213 Identities (dpeaa)DE-He213 Non-exponential family (dpeaa)DE-He213 Non-normal distributions (dpeaa)DE-He213 Poisson approximation (dpeaa)DE-He213 Shrinkage estimation (dpeaa)DE-He213 Stein identity (dpeaa)DE-He213 SURE (dpeaa)DE-He213 |
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ddc 004 bkl 31.70 bkl 31.80 misc Chen-Stein approximation misc Continuous distributions misc Cramér-Rao identity misc Exponential family misc Identities misc Non-exponential family misc Non-normal distributions misc Poisson approximation misc Shrinkage estimation misc Stein identity misc SURE |
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On Rereading Stein’s Lemma: Its Intrinsic Connection with Cramér-Rao Identity and Some New Identities |
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on rereading stein’s lemma: its intrinsic connection with cramér-rao identity and some new identities |
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On Rereading Stein’s Lemma: Its Intrinsic Connection with Cramér-Rao Identity and Some New Identities |
| abstract |
Abstract Now is an opportune time to revisit Stein’s (1973) beautiful lemma all over again. It is especially so since researchers have recently begun discovering a great deal of potential of closely related Stein’s unbiased risk estimate (SURE) in a number of directions involving novel applications. In recognition of the importance of the topic of Stein’s (1973; Ann Statist 9:1135–1151, 1981) research and its elegance, we include a selective review from the field. The process of rereading Stein’s lemma and reliving its awesome simplicity as well as versatility rekindled a number of personal thoughts, queries, and observations. A number of new and interesting insights are highlighted in the spirit of providing updated and futuristic versions of the celebrated lemma by largely focusing on univariate continuous distributions not belonging to an exponential family. In doing so, a number of new identities have emerged when the parent population is continuous, but they are highly non-normal. Last, but not the least, we have argued that there is no big foundational difference between the basic messages obtained via Stein’s identity and Cramér-Rao identity. |
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Abstract Now is an opportune time to revisit Stein’s (1973) beautiful lemma all over again. It is especially so since researchers have recently begun discovering a great deal of potential of closely related Stein’s unbiased risk estimate (SURE) in a number of directions involving novel applications. In recognition of the importance of the topic of Stein’s (1973; Ann Statist 9:1135–1151, 1981) research and its elegance, we include a selective review from the field. The process of rereading Stein’s lemma and reliving its awesome simplicity as well as versatility rekindled a number of personal thoughts, queries, and observations. A number of new and interesting insights are highlighted in the spirit of providing updated and futuristic versions of the celebrated lemma by largely focusing on univariate continuous distributions not belonging to an exponential family. In doing so, a number of new identities have emerged when the parent population is continuous, but they are highly non-normal. Last, but not the least, we have argued that there is no big foundational difference between the basic messages obtained via Stein’s identity and Cramér-Rao identity. |
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Abstract Now is an opportune time to revisit Stein’s (1973) beautiful lemma all over again. It is especially so since researchers have recently begun discovering a great deal of potential of closely related Stein’s unbiased risk estimate (SURE) in a number of directions involving novel applications. In recognition of the importance of the topic of Stein’s (1973; Ann Statist 9:1135–1151, 1981) research and its elegance, we include a selective review from the field. The process of rereading Stein’s lemma and reliving its awesome simplicity as well as versatility rekindled a number of personal thoughts, queries, and observations. A number of new and interesting insights are highlighted in the spirit of providing updated and futuristic versions of the celebrated lemma by largely focusing on univariate continuous distributions not belonging to an exponential family. In doing so, a number of new identities have emerged when the parent population is continuous, but they are highly non-normal. Last, but not the least, we have argued that there is no big foundational difference between the basic messages obtained via Stein’s identity and Cramér-Rao identity. |
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| score |
7.4021006 |