Optimal variance estimation based on lagged second-order difference in nonparametric regression
Abstract Differenced estimators of variance bypass the estimation of regression function and thus are simple to calculate. However, there exist two problems: most differenced estimators do not achieve the asymptotic optimal rate for the mean square error; for finite samples the estimation bias is al...
Ausführliche Beschreibung
Autor*in: |
Wang, WenWu [verfasserIn] |
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Format: |
E-Artikel |
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Sprache: |
Englisch |
Erschienen: |
2016 |
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Schlagwörter: |
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Anmerkung: |
© The Author(s) 2016 |
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Übergeordnetes Werk: |
Enthalten in: Computational statistics - Berlin : Springer, 1999, 32(2016), 3 vom: 21. Juni, Seite 1047-1063 |
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Übergeordnetes Werk: |
volume:32 ; year:2016 ; number:3 ; day:21 ; month:06 ; pages:1047-1063 |
Links: |
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DOI / URN: |
10.1007/s00180-016-0666-2 |
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Katalog-ID: |
SPR001518461 |
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520 | |a Abstract Differenced estimators of variance bypass the estimation of regression function and thus are simple to calculate. However, there exist two problems: most differenced estimators do not achieve the asymptotic optimal rate for the mean square error; for finite samples the estimation bias is also important and not further considered. In this paper, we estimate the variance as the intercept in a linear regression with the lagged Gasser-type variance estimator as dependent variable. For the equidistant design, our estimator is not only %$n^{1/2}%$-consistent and asymptotically normal, but also achieves the optimal bound in terms of estimation variance with less asymptotic bias. Simulation studies show that our estimator has less mean square error than some existing differenced estimators, especially in the cases of immense oscillation of regression function and small-sized sample. | ||
650 | 4 | |a Least squares |7 (dpeaa)DE-He213 | |
650 | 4 | |a Nonparametric variance estimation |7 (dpeaa)DE-He213 | |
650 | 4 | |a Optimal differenced estimator |7 (dpeaa)DE-He213 | |
700 | 1 | |a Lin, Lu |4 aut | |
700 | 1 | |a Yu, Li |4 aut | |
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10.1007/s00180-016-0666-2 doi (DE-627)SPR001518461 (SPR)s00180-016-0666-2-e DE-627 ger DE-627 rakwb eng Wang, WenWu verfasserin aut Optimal variance estimation based on lagged second-order difference in nonparametric regression 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2016 Abstract Differenced estimators of variance bypass the estimation of regression function and thus are simple to calculate. However, there exist two problems: most differenced estimators do not achieve the asymptotic optimal rate for the mean square error; for finite samples the estimation bias is also important and not further considered. In this paper, we estimate the variance as the intercept in a linear regression with the lagged Gasser-type variance estimator as dependent variable. For the equidistant design, our estimator is not only %$n^{1/2}%$-consistent and asymptotically normal, but also achieves the optimal bound in terms of estimation variance with less asymptotic bias. Simulation studies show that our estimator has less mean square error than some existing differenced estimators, especially in the cases of immense oscillation of regression function and small-sized sample. Least squares (dpeaa)DE-He213 Nonparametric variance estimation (dpeaa)DE-He213 Optimal differenced estimator (dpeaa)DE-He213 Lin, Lu aut Yu, Li aut Enthalten in Computational statistics Berlin : Springer, 1999 32(2016), 3 vom: 21. Juni, Seite 1047-1063 (DE-627)271599170 (DE-600)1480911-4 1613-9658 nnns volume:32 year:2016 number:3 day:21 month:06 pages:1047-1063 https://dx.doi.org/10.1007/s00180-016-0666-2 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_65 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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_4012 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 AR 32 2016 3 21 06 1047-1063 |
spelling |
10.1007/s00180-016-0666-2 doi (DE-627)SPR001518461 (SPR)s00180-016-0666-2-e DE-627 ger DE-627 rakwb eng Wang, WenWu verfasserin aut Optimal variance estimation based on lagged second-order difference in nonparametric regression 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2016 Abstract Differenced estimators of variance bypass the estimation of regression function and thus are simple to calculate. However, there exist two problems: most differenced estimators do not achieve the asymptotic optimal rate for the mean square error; for finite samples the estimation bias is also important and not further considered. In this paper, we estimate the variance as the intercept in a linear regression with the lagged Gasser-type variance estimator as dependent variable. For the equidistant design, our estimator is not only %$n^{1/2}%$-consistent and asymptotically normal, but also achieves the optimal bound in terms of estimation variance with less asymptotic bias. Simulation studies show that our estimator has less mean square error than some existing differenced estimators, especially in the cases of immense oscillation of regression function and small-sized sample. Least squares (dpeaa)DE-He213 Nonparametric variance estimation (dpeaa)DE-He213 Optimal differenced estimator (dpeaa)DE-He213 Lin, Lu aut Yu, Li aut Enthalten in Computational statistics Berlin : Springer, 1999 32(2016), 3 vom: 21. Juni, Seite 1047-1063 (DE-627)271599170 (DE-600)1480911-4 1613-9658 nnns volume:32 year:2016 number:3 day:21 month:06 pages:1047-1063 https://dx.doi.org/10.1007/s00180-016-0666-2 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_65 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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_4012 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 AR 32 2016 3 21 06 1047-1063 |
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10.1007/s00180-016-0666-2 doi (DE-627)SPR001518461 (SPR)s00180-016-0666-2-e DE-627 ger DE-627 rakwb eng Wang, WenWu verfasserin aut Optimal variance estimation based on lagged second-order difference in nonparametric regression 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2016 Abstract Differenced estimators of variance bypass the estimation of regression function and thus are simple to calculate. However, there exist two problems: most differenced estimators do not achieve the asymptotic optimal rate for the mean square error; for finite samples the estimation bias is also important and not further considered. In this paper, we estimate the variance as the intercept in a linear regression with the lagged Gasser-type variance estimator as dependent variable. For the equidistant design, our estimator is not only %$n^{1/2}%$-consistent and asymptotically normal, but also achieves the optimal bound in terms of estimation variance with less asymptotic bias. Simulation studies show that our estimator has less mean square error than some existing differenced estimators, especially in the cases of immense oscillation of regression function and small-sized sample. Least squares (dpeaa)DE-He213 Nonparametric variance estimation (dpeaa)DE-He213 Optimal differenced estimator (dpeaa)DE-He213 Lin, Lu aut Yu, Li aut Enthalten in Computational statistics Berlin : Springer, 1999 32(2016), 3 vom: 21. Juni, Seite 1047-1063 (DE-627)271599170 (DE-600)1480911-4 1613-9658 nnns volume:32 year:2016 number:3 day:21 month:06 pages:1047-1063 https://dx.doi.org/10.1007/s00180-016-0666-2 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_65 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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_4012 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 AR 32 2016 3 21 06 1047-1063 |
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10.1007/s00180-016-0666-2 doi (DE-627)SPR001518461 (SPR)s00180-016-0666-2-e DE-627 ger DE-627 rakwb eng Wang, WenWu verfasserin aut Optimal variance estimation based on lagged second-order difference in nonparametric regression 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2016 Abstract Differenced estimators of variance bypass the estimation of regression function and thus are simple to calculate. However, there exist two problems: most differenced estimators do not achieve the asymptotic optimal rate for the mean square error; for finite samples the estimation bias is also important and not further considered. In this paper, we estimate the variance as the intercept in a linear regression with the lagged Gasser-type variance estimator as dependent variable. For the equidistant design, our estimator is not only %$n^{1/2}%$-consistent and asymptotically normal, but also achieves the optimal bound in terms of estimation variance with less asymptotic bias. Simulation studies show that our estimator has less mean square error than some existing differenced estimators, especially in the cases of immense oscillation of regression function and small-sized sample. Least squares (dpeaa)DE-He213 Nonparametric variance estimation (dpeaa)DE-He213 Optimal differenced estimator (dpeaa)DE-He213 Lin, Lu aut Yu, Li aut Enthalten in Computational statistics Berlin : Springer, 1999 32(2016), 3 vom: 21. Juni, Seite 1047-1063 (DE-627)271599170 (DE-600)1480911-4 1613-9658 nnns volume:32 year:2016 number:3 day:21 month:06 pages:1047-1063 https://dx.doi.org/10.1007/s00180-016-0666-2 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_65 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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_4012 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 AR 32 2016 3 21 06 1047-1063 |
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10.1007/s00180-016-0666-2 doi (DE-627)SPR001518461 (SPR)s00180-016-0666-2-e DE-627 ger DE-627 rakwb eng Wang, WenWu verfasserin aut Optimal variance estimation based on lagged second-order difference in nonparametric regression 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2016 Abstract Differenced estimators of variance bypass the estimation of regression function and thus are simple to calculate. However, there exist two problems: most differenced estimators do not achieve the asymptotic optimal rate for the mean square error; for finite samples the estimation bias is also important and not further considered. In this paper, we estimate the variance as the intercept in a linear regression with the lagged Gasser-type variance estimator as dependent variable. For the equidistant design, our estimator is not only %$n^{1/2}%$-consistent and asymptotically normal, but also achieves the optimal bound in terms of estimation variance with less asymptotic bias. Simulation studies show that our estimator has less mean square error than some existing differenced estimators, especially in the cases of immense oscillation of regression function and small-sized sample. Least squares (dpeaa)DE-He213 Nonparametric variance estimation (dpeaa)DE-He213 Optimal differenced estimator (dpeaa)DE-He213 Lin, Lu aut Yu, Li aut Enthalten in Computational statistics Berlin : Springer, 1999 32(2016), 3 vom: 21. Juni, Seite 1047-1063 (DE-627)271599170 (DE-600)1480911-4 1613-9658 nnns volume:32 year:2016 number:3 day:21 month:06 pages:1047-1063 https://dx.doi.org/10.1007/s00180-016-0666-2 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_65 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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_4012 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 AR 32 2016 3 21 06 1047-1063 |
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Enthalten in Computational statistics 32(2016), 3 vom: 21. Juni, Seite 1047-1063 volume:32 year:2016 number:3 day:21 month:06 pages:1047-1063 |
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Wang, WenWu @@aut@@ Lin, Lu @@aut@@ Yu, Li @@aut@@ |
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Wang, WenWu misc Least squares misc Nonparametric variance estimation misc Optimal differenced estimator Optimal variance estimation based on lagged second-order difference in nonparametric regression |
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Optimal variance estimation based on lagged second-order difference in nonparametric regression Least squares (dpeaa)DE-He213 Nonparametric variance estimation (dpeaa)DE-He213 Optimal differenced estimator (dpeaa)DE-He213 |
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optimal variance estimation based on lagged second-order difference in nonparametric regression |
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Optimal variance estimation based on lagged second-order difference in nonparametric regression |
abstract |
Abstract Differenced estimators of variance bypass the estimation of regression function and thus are simple to calculate. However, there exist two problems: most differenced estimators do not achieve the asymptotic optimal rate for the mean square error; for finite samples the estimation bias is also important and not further considered. In this paper, we estimate the variance as the intercept in a linear regression with the lagged Gasser-type variance estimator as dependent variable. For the equidistant design, our estimator is not only %$n^{1/2}%$-consistent and asymptotically normal, but also achieves the optimal bound in terms of estimation variance with less asymptotic bias. Simulation studies show that our estimator has less mean square error than some existing differenced estimators, especially in the cases of immense oscillation of regression function and small-sized sample. © The Author(s) 2016 |
abstractGer |
Abstract Differenced estimators of variance bypass the estimation of regression function and thus are simple to calculate. However, there exist two problems: most differenced estimators do not achieve the asymptotic optimal rate for the mean square error; for finite samples the estimation bias is also important and not further considered. In this paper, we estimate the variance as the intercept in a linear regression with the lagged Gasser-type variance estimator as dependent variable. For the equidistant design, our estimator is not only %$n^{1/2}%$-consistent and asymptotically normal, but also achieves the optimal bound in terms of estimation variance with less asymptotic bias. Simulation studies show that our estimator has less mean square error than some existing differenced estimators, especially in the cases of immense oscillation of regression function and small-sized sample. © The Author(s) 2016 |
abstract_unstemmed |
Abstract Differenced estimators of variance bypass the estimation of regression function and thus are simple to calculate. However, there exist two problems: most differenced estimators do not achieve the asymptotic optimal rate for the mean square error; for finite samples the estimation bias is also important and not further considered. In this paper, we estimate the variance as the intercept in a linear regression with the lagged Gasser-type variance estimator as dependent variable. For the equidistant design, our estimator is not only %$n^{1/2}%$-consistent and asymptotically normal, but also achieves the optimal bound in terms of estimation variance with less asymptotic bias. Simulation studies show that our estimator has less mean square error than some existing differenced estimators, especially in the cases of immense oscillation of regression function and small-sized sample. © The Author(s) 2016 |
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Optimal variance estimation based on lagged second-order difference in nonparametric regression |
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However, there exist two problems: most differenced estimators do not achieve the asymptotic optimal rate for the mean square error; for finite samples the estimation bias is also important and not further considered. In this paper, we estimate the variance as the intercept in a linear regression with the lagged Gasser-type variance estimator as dependent variable. For the equidistant design, our estimator is not only %$n^{1/2}%$-consistent and asymptotically normal, but also achieves the optimal bound in terms of estimation variance with less asymptotic bias. 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