Nonparametric estimation of cumulative distribution function from noisy data in the presence of Berkson and classical errors
Abstract Let X, Y, W, %$\delta %$ and %$\varepsilon %$ be continuous univariate random variables defined on a probability space such that %$Y = X+\varepsilon %$ and %$W = X + \delta %$. Herein X, %$\delta %$ and %$\varepsilon %$ are assumed to be mutually independent. The variables %$\varepsilon %$...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Phuong, Cao Xuan [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2021 |
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| Anmerkung: |
© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021 |
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| Übergeordnetes Werk: |
Enthalten in: Metrika - Berlin : Springer, 1958, 85(2021), 3 vom: 09. Juli, Seite 289-322 |
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| Übergeordnetes Werk: |
volume:85 ; year:2021 ; number:3 ; day:09 ; month:07 ; pages:289-322 |
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| DOI / URN: |
10.1007/s00184-021-00830-5 |
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| Katalog-ID: |
SPR046370773 |
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| 100 | 1 | |a Phuong, Cao Xuan |e verfasserin |0 (orcid)0000-0002-2943-1096 |4 aut | |
| 245 | 1 | 0 | |a Nonparametric estimation of cumulative distribution function from noisy data in the presence of Berkson and classical errors |
| 264 | 1 | |c 2021 | |
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| 500 | |a © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021 | ||
| 520 | |a Abstract Let X, Y, W, %$\delta %$ and %$\varepsilon %$ be continuous univariate random variables defined on a probability space such that %$Y = X+\varepsilon %$ and %$W = X + \delta %$. Herein X, %$\delta %$ and %$\varepsilon %$ are assumed to be mutually independent. The variables %$\varepsilon %$ and %$\delta %$ are called classical and Berkson errors, respectively. Their distributions are known exactly. Suppose we only observe a random sample %$Y_1, \ldots , Y_n%$ from the distribution of Y. This paper is devoted to a nonparametric estimation of the unknown cumulative distribution function %$F_W%$ of W based on the observations as well as on the distributions of %$\varepsilon %$, %$\delta %$. An estimator for %$F_W%$ depending on a smoothing parameter is suggested. It is shown to be consistent with respect to the mean squared error. Under certain regularity assumptions on the densities of X, %$\delta %$ and %$\varepsilon %$, we establish some upper and lower bounds on the convergence rate of the proposed estimator. Finally, we perform some numerical examples to illustrate our theoretical results. | ||
| 650 | 4 | |a Cumulative distribution function |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Deconvolution |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Berkson errors |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Classical errors |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Thuy, Le Thi Hong |0 (orcid)0000-0003-1085-8505 |4 aut | |
| 700 | 1 | |a Doan, Vo Nguyen Tuyet |0 (orcid)0000-0002-2156-4708 |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Metrika |d Berlin : Springer, 1958 |g 85(2021), 3 vom: 09. Juli, Seite 289-322 |w (DE-627)254630952 |w (DE-600)1462149-6 |x 1435-926X |7 nnns |
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10.1007/s00184-021-00830-5 doi (DE-627)SPR046370773 (SPR)s00184-021-00830-5-e DE-627 ger DE-627 rakwb eng Phuong, Cao Xuan verfasserin (orcid)0000-0002-2943-1096 aut Nonparametric estimation of cumulative distribution function from noisy data in the presence of Berkson and classical errors 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021 Abstract Let X, Y, W, %$\delta %$ and %$\varepsilon %$ be continuous univariate random variables defined on a probability space such that %$Y = X+\varepsilon %$ and %$W = X + \delta %$. Herein X, %$\delta %$ and %$\varepsilon %$ are assumed to be mutually independent. The variables %$\varepsilon %$ and %$\delta %$ are called classical and Berkson errors, respectively. Their distributions are known exactly. Suppose we only observe a random sample %$Y_1, \ldots , Y_n%$ from the distribution of Y. This paper is devoted to a nonparametric estimation of the unknown cumulative distribution function %$F_W%$ of W based on the observations as well as on the distributions of %$\varepsilon %$, %$\delta %$. An estimator for %$F_W%$ depending on a smoothing parameter is suggested. It is shown to be consistent with respect to the mean squared error. Under certain regularity assumptions on the densities of X, %$\delta %$ and %$\varepsilon %$, we establish some upper and lower bounds on the convergence rate of the proposed estimator. Finally, we perform some numerical examples to illustrate our theoretical results. Cumulative distribution function (dpeaa)DE-He213 Deconvolution (dpeaa)DE-He213 Berkson errors (dpeaa)DE-He213 Classical errors (dpeaa)DE-He213 Thuy, Le Thi Hong (orcid)0000-0003-1085-8505 aut Doan, Vo Nguyen Tuyet (orcid)0000-0002-2156-4708 aut Enthalten in Metrika Berlin : Springer, 1958 85(2021), 3 vom: 09. Juli, Seite 289-322 (DE-627)254630952 (DE-600)1462149-6 1435-926X nnns volume:85 year:2021 number:3 day:09 month:07 pages:289-322 https://dx.doi.org/10.1007/s00184-021-00830-5 lizenzpflichtig 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_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_267 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 AR 85 2021 3 09 07 289-322 |
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10.1007/s00184-021-00830-5 doi (DE-627)SPR046370773 (SPR)s00184-021-00830-5-e DE-627 ger DE-627 rakwb eng Phuong, Cao Xuan verfasserin (orcid)0000-0002-2943-1096 aut Nonparametric estimation of cumulative distribution function from noisy data in the presence of Berkson and classical errors 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021 Abstract Let X, Y, W, %$\delta %$ and %$\varepsilon %$ be continuous univariate random variables defined on a probability space such that %$Y = X+\varepsilon %$ and %$W = X + \delta %$. Herein X, %$\delta %$ and %$\varepsilon %$ are assumed to be mutually independent. The variables %$\varepsilon %$ and %$\delta %$ are called classical and Berkson errors, respectively. Their distributions are known exactly. Suppose we only observe a random sample %$Y_1, \ldots , Y_n%$ from the distribution of Y. This paper is devoted to a nonparametric estimation of the unknown cumulative distribution function %$F_W%$ of W based on the observations as well as on the distributions of %$\varepsilon %$, %$\delta %$. An estimator for %$F_W%$ depending on a smoothing parameter is suggested. It is shown to be consistent with respect to the mean squared error. Under certain regularity assumptions on the densities of X, %$\delta %$ and %$\varepsilon %$, we establish some upper and lower bounds on the convergence rate of the proposed estimator. Finally, we perform some numerical examples to illustrate our theoretical results. Cumulative distribution function (dpeaa)DE-He213 Deconvolution (dpeaa)DE-He213 Berkson errors (dpeaa)DE-He213 Classical errors (dpeaa)DE-He213 Thuy, Le Thi Hong (orcid)0000-0003-1085-8505 aut Doan, Vo Nguyen Tuyet (orcid)0000-0002-2156-4708 aut Enthalten in Metrika Berlin : Springer, 1958 85(2021), 3 vom: 09. Juli, Seite 289-322 (DE-627)254630952 (DE-600)1462149-6 1435-926X nnns volume:85 year:2021 number:3 day:09 month:07 pages:289-322 https://dx.doi.org/10.1007/s00184-021-00830-5 lizenzpflichtig 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_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_267 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 AR 85 2021 3 09 07 289-322 |
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10.1007/s00184-021-00830-5 doi (DE-627)SPR046370773 (SPR)s00184-021-00830-5-e DE-627 ger DE-627 rakwb eng Phuong, Cao Xuan verfasserin (orcid)0000-0002-2943-1096 aut Nonparametric estimation of cumulative distribution function from noisy data in the presence of Berkson and classical errors 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021 Abstract Let X, Y, W, %$\delta %$ and %$\varepsilon %$ be continuous univariate random variables defined on a probability space such that %$Y = X+\varepsilon %$ and %$W = X + \delta %$. Herein X, %$\delta %$ and %$\varepsilon %$ are assumed to be mutually independent. The variables %$\varepsilon %$ and %$\delta %$ are called classical and Berkson errors, respectively. Their distributions are known exactly. Suppose we only observe a random sample %$Y_1, \ldots , Y_n%$ from the distribution of Y. This paper is devoted to a nonparametric estimation of the unknown cumulative distribution function %$F_W%$ of W based on the observations as well as on the distributions of %$\varepsilon %$, %$\delta %$. An estimator for %$F_W%$ depending on a smoothing parameter is suggested. It is shown to be consistent with respect to the mean squared error. Under certain regularity assumptions on the densities of X, %$\delta %$ and %$\varepsilon %$, we establish some upper and lower bounds on the convergence rate of the proposed estimator. Finally, we perform some numerical examples to illustrate our theoretical results. Cumulative distribution function (dpeaa)DE-He213 Deconvolution (dpeaa)DE-He213 Berkson errors (dpeaa)DE-He213 Classical errors (dpeaa)DE-He213 Thuy, Le Thi Hong (orcid)0000-0003-1085-8505 aut Doan, Vo Nguyen Tuyet (orcid)0000-0002-2156-4708 aut Enthalten in Metrika Berlin : Springer, 1958 85(2021), 3 vom: 09. Juli, Seite 289-322 (DE-627)254630952 (DE-600)1462149-6 1435-926X nnns volume:85 year:2021 number:3 day:09 month:07 pages:289-322 https://dx.doi.org/10.1007/s00184-021-00830-5 lizenzpflichtig 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_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_267 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 AR 85 2021 3 09 07 289-322 |
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10.1007/s00184-021-00830-5 doi (DE-627)SPR046370773 (SPR)s00184-021-00830-5-e DE-627 ger DE-627 rakwb eng Phuong, Cao Xuan verfasserin (orcid)0000-0002-2943-1096 aut Nonparametric estimation of cumulative distribution function from noisy data in the presence of Berkson and classical errors 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021 Abstract Let X, Y, W, %$\delta %$ and %$\varepsilon %$ be continuous univariate random variables defined on a probability space such that %$Y = X+\varepsilon %$ and %$W = X + \delta %$. Herein X, %$\delta %$ and %$\varepsilon %$ are assumed to be mutually independent. The variables %$\varepsilon %$ and %$\delta %$ are called classical and Berkson errors, respectively. Their distributions are known exactly. Suppose we only observe a random sample %$Y_1, \ldots , Y_n%$ from the distribution of Y. This paper is devoted to a nonparametric estimation of the unknown cumulative distribution function %$F_W%$ of W based on the observations as well as on the distributions of %$\varepsilon %$, %$\delta %$. An estimator for %$F_W%$ depending on a smoothing parameter is suggested. It is shown to be consistent with respect to the mean squared error. Under certain regularity assumptions on the densities of X, %$\delta %$ and %$\varepsilon %$, we establish some upper and lower bounds on the convergence rate of the proposed estimator. Finally, we perform some numerical examples to illustrate our theoretical results. Cumulative distribution function (dpeaa)DE-He213 Deconvolution (dpeaa)DE-He213 Berkson errors (dpeaa)DE-He213 Classical errors (dpeaa)DE-He213 Thuy, Le Thi Hong (orcid)0000-0003-1085-8505 aut Doan, Vo Nguyen Tuyet (orcid)0000-0002-2156-4708 aut Enthalten in Metrika Berlin : Springer, 1958 85(2021), 3 vom: 09. Juli, Seite 289-322 (DE-627)254630952 (DE-600)1462149-6 1435-926X nnns volume:85 year:2021 number:3 day:09 month:07 pages:289-322 https://dx.doi.org/10.1007/s00184-021-00830-5 lizenzpflichtig 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_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_267 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 AR 85 2021 3 09 07 289-322 |
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10.1007/s00184-021-00830-5 doi (DE-627)SPR046370773 (SPR)s00184-021-00830-5-e DE-627 ger DE-627 rakwb eng Phuong, Cao Xuan verfasserin (orcid)0000-0002-2943-1096 aut Nonparametric estimation of cumulative distribution function from noisy data in the presence of Berkson and classical errors 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021 Abstract Let X, Y, W, %$\delta %$ and %$\varepsilon %$ be continuous univariate random variables defined on a probability space such that %$Y = X+\varepsilon %$ and %$W = X + \delta %$. Herein X, %$\delta %$ and %$\varepsilon %$ are assumed to be mutually independent. The variables %$\varepsilon %$ and %$\delta %$ are called classical and Berkson errors, respectively. Their distributions are known exactly. Suppose we only observe a random sample %$Y_1, \ldots , Y_n%$ from the distribution of Y. This paper is devoted to a nonparametric estimation of the unknown cumulative distribution function %$F_W%$ of W based on the observations as well as on the distributions of %$\varepsilon %$, %$\delta %$. An estimator for %$F_W%$ depending on a smoothing parameter is suggested. It is shown to be consistent with respect to the mean squared error. Under certain regularity assumptions on the densities of X, %$\delta %$ and %$\varepsilon %$, we establish some upper and lower bounds on the convergence rate of the proposed estimator. Finally, we perform some numerical examples to illustrate our theoretical results. Cumulative distribution function (dpeaa)DE-He213 Deconvolution (dpeaa)DE-He213 Berkson errors (dpeaa)DE-He213 Classical errors (dpeaa)DE-He213 Thuy, Le Thi Hong (orcid)0000-0003-1085-8505 aut Doan, Vo Nguyen Tuyet (orcid)0000-0002-2156-4708 aut Enthalten in Metrika Berlin : Springer, 1958 85(2021), 3 vom: 09. Juli, Seite 289-322 (DE-627)254630952 (DE-600)1462149-6 1435-926X nnns volume:85 year:2021 number:3 day:09 month:07 pages:289-322 https://dx.doi.org/10.1007/s00184-021-00830-5 lizenzpflichtig 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_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_267 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 AR 85 2021 3 09 07 289-322 |
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Phuong, Cao Xuan @@aut@@ Thuy, Le Thi Hong @@aut@@ Doan, Vo Nguyen Tuyet @@aut@@ |
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Herein X, %$\delta %$ and %$\varepsilon %$ are assumed to be mutually independent. The variables %$\varepsilon %$ and %$\delta %$ are called classical and Berkson errors, respectively. Their distributions are known exactly. Suppose we only observe a random sample %$Y_1, \ldots , Y_n%$ from the distribution of Y. This paper is devoted to a nonparametric estimation of the unknown cumulative distribution function %$F_W%$ of W based on the observations as well as on the distributions of %$\varepsilon %$, %$\delta %$. An estimator for %$F_W%$ depending on a smoothing parameter is suggested. It is shown to be consistent with respect to the mean squared error. Under certain regularity assumptions on the densities of X, %$\delta %$ and %$\varepsilon %$, we establish some upper and lower bounds on the convergence rate of the proposed estimator. 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Phuong, Cao Xuan |
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Nonparametric estimation of cumulative distribution function from noisy data in the presence of Berkson and classical errors Cumulative distribution function (dpeaa)DE-He213 Deconvolution (dpeaa)DE-He213 Berkson errors (dpeaa)DE-He213 Classical errors (dpeaa)DE-He213 |
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nonparametric estimation of cumulative distribution function from noisy data in the presence of berkson and classical errors |
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Nonparametric estimation of cumulative distribution function from noisy data in the presence of Berkson and classical errors |
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Abstract Let X, Y, W, %$\delta %$ and %$\varepsilon %$ be continuous univariate random variables defined on a probability space such that %$Y = X+\varepsilon %$ and %$W = X + \delta %$. Herein X, %$\delta %$ and %$\varepsilon %$ are assumed to be mutually independent. The variables %$\varepsilon %$ and %$\delta %$ are called classical and Berkson errors, respectively. Their distributions are known exactly. Suppose we only observe a random sample %$Y_1, \ldots , Y_n%$ from the distribution of Y. This paper is devoted to a nonparametric estimation of the unknown cumulative distribution function %$F_W%$ of W based on the observations as well as on the distributions of %$\varepsilon %$, %$\delta %$. An estimator for %$F_W%$ depending on a smoothing parameter is suggested. It is shown to be consistent with respect to the mean squared error. Under certain regularity assumptions on the densities of X, %$\delta %$ and %$\varepsilon %$, we establish some upper and lower bounds on the convergence rate of the proposed estimator. Finally, we perform some numerical examples to illustrate our theoretical results. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021 |
| abstractGer |
Abstract Let X, Y, W, %$\delta %$ and %$\varepsilon %$ be continuous univariate random variables defined on a probability space such that %$Y = X+\varepsilon %$ and %$W = X + \delta %$. Herein X, %$\delta %$ and %$\varepsilon %$ are assumed to be mutually independent. The variables %$\varepsilon %$ and %$\delta %$ are called classical and Berkson errors, respectively. Their distributions are known exactly. Suppose we only observe a random sample %$Y_1, \ldots , Y_n%$ from the distribution of Y. This paper is devoted to a nonparametric estimation of the unknown cumulative distribution function %$F_W%$ of W based on the observations as well as on the distributions of %$\varepsilon %$, %$\delta %$. An estimator for %$F_W%$ depending on a smoothing parameter is suggested. It is shown to be consistent with respect to the mean squared error. Under certain regularity assumptions on the densities of X, %$\delta %$ and %$\varepsilon %$, we establish some upper and lower bounds on the convergence rate of the proposed estimator. Finally, we perform some numerical examples to illustrate our theoretical results. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021 |
| abstract_unstemmed |
Abstract Let X, Y, W, %$\delta %$ and %$\varepsilon %$ be continuous univariate random variables defined on a probability space such that %$Y = X+\varepsilon %$ and %$W = X + \delta %$. Herein X, %$\delta %$ and %$\varepsilon %$ are assumed to be mutually independent. The variables %$\varepsilon %$ and %$\delta %$ are called classical and Berkson errors, respectively. Their distributions are known exactly. Suppose we only observe a random sample %$Y_1, \ldots , Y_n%$ from the distribution of Y. This paper is devoted to a nonparametric estimation of the unknown cumulative distribution function %$F_W%$ of W based on the observations as well as on the distributions of %$\varepsilon %$, %$\delta %$. An estimator for %$F_W%$ depending on a smoothing parameter is suggested. It is shown to be consistent with respect to the mean squared error. Under certain regularity assumptions on the densities of X, %$\delta %$ and %$\varepsilon %$, we establish some upper and lower bounds on the convergence rate of the proposed estimator. Finally, we perform some numerical examples to illustrate our theoretical results. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021 |
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Nonparametric estimation of cumulative distribution function from noisy data in the presence of Berkson and classical errors |
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https://dx.doi.org/10.1007/s00184-021-00830-5 |
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Thuy, Le Thi Hong Doan, Vo Nguyen Tuyet |
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10.1007/s00184-021-00830-5 |
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2024-07-03T22:07:44.126Z |
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| score |
7.4014053 |