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Volumn 37, Issue 6 A, 2009, Pages 3204-3235

Asymptotic equivalence and adaptive estimation fo1 robust nonparametric regression

Author keywords

Adaptivity; Asymptotic equivalence; James Stein estimator; Moderate deviation; Nonparametric regression; Quantile coupling; Robust estimation; Unbounded loss function; Wavelets

Indexed keywords


EID: 70049114041     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/08-AOS681     Document Type: Article
Times cited : (13)

References (50)
  • 1
    • 0001667487 scopus 로고
    • Estimating integrated squared density derivatives: Sharp best order of convergence estimates
    • MR1065550
    • Bickel, P. J. and Ritov, Y. (1988). Estimating integrated squared density derivatives: Sharp best order of convergence estimates. Sankhyã Ser. A 50 381-393. MR1065550
    • (1988) Sankhyã Ser. A , vol.50 , pp. 381-393
    • Bickel, P.J.1    Ritov, Y.2
  • 2
    • 0036048503 scopus 로고    scopus 로고
    • Asymptotic equivalence theory for nonparametric regression with random design
    • MR1922538
    • Brown, L.D., Cai, T.T., Low, M.G. and Zhang, C. (2002). Asymptotic equivalence theory for nonparametric regression with random design. Ann. Statist. 30 688-707. MR1922538
    • (2002) Ann. Statist , vol.30 , pp. 688-707
    • Brown, L.D.1    Cai, T.T.2    Low, M.G.3    Zhang, C.4
  • 3
    • 54349125331 scopus 로고    scopus 로고
    • Robust nonparametric estimation via wavelet median regression
    • MR2458179
    • Brown, L.D., Cai, T.T. and Zhou, H. H. (2008). Robust nonparametric estimation via wavelet median regression. Ann. Statist. 36 2055-2084. MR2458179
    • (2008) Ann. Statist , vol.36 , pp. 2055-2084
    • Brown, L.D.1    Cai, T.T.2    Zhou, H.H.3
  • 4
    • 21644472518 scopus 로고    scopus 로고
    • Equivalence theory for density estimation, Poisson processes and Gaussian white noise with drift
    • MR2102503
    • Brown, L. D., Carter, A. V., Low, M.G. and Zhang, C.-H. (2004). Equivalence theory for density estimation, Poisson processes and Gaussian white noise with drift. Ann. Statist. 32 2074-2097. MR2102503
    • (2004) Ann. Statist , vol.32 , pp. 2074-2097
    • Brown, L.D.1    Carter, A.V.2    Low, M.G.3    Zhang, C.-H.4
  • 5
    • 0030327799 scopus 로고    scopus 로고
    • A constrained risk inequality with applications to nonparametric functional estimation
    • MR1425965
    • Brown L. D. and Low, M. G. (1996a). A constrained risk inequality with applications to nonparametric functional estimation. Ann. Statist. 24 2524-2535. MR1425965
    • (1996) Ann. Statist , vol.24 , pp. 2524-2535
    • Brown, L.D.1    Low, M.G.2
  • 6
    • 0030335402 scopus 로고    scopus 로고
    • Asymptotic equivalence of nonparametric regression and white noise
    • MR1425958
    • Brown, L.D. andLow, M. G. (1996b). Asymptotic equivalence of nonparametric regression and white noise. Ann. Statist. 24 2384-2398. MR1425958
    • (1996) Ann. Statist , vol.24 , pp. 2384-2398
    • Brown, L.D.1    G, M.2
  • 7
    • 0346968381 scopus 로고    scopus 로고
    • Statistical equivalence at suitable frequencies of GARCH and stochastic volatility models with the corresponding diffusion model
    • MR2026059
    • Brown, L.D., Wang, Y. and Zhao, L. (2003). Statistical equivalence at suitable frequencies of GARCH and stochastic volatility models with the corresponding diffusion model. Statist. Sinica 13 993-1013. MR2026059
    • (2003) Statist. Sinica , vol.13 , pp. 993-1013
    • Brown, L.D.1    Wang, Y.2    Zhao, L.3
  • 8
    • 0033248624 scopus 로고    scopus 로고
    • Adaptive wavelet estimation: A block thresholding and oracle inequality approach
    • MR1724035
    • Cai, T. (1999). Adaptive wavelet estimation: A block thresholding and oracle inequality approach. Ann. Statist. 27 898-924. MR1724035
    • (1999) Ann. Statist , vol.27 , pp. 898-924
    • Cai, T.1
  • 9
    • 33644915542 scopus 로고    scopus 로고
    • Nonquadratic estimators of a quadratic functional
    • MR2253108
    • Cai, T.andLow, M. (2005). Nonquadratic estimators of a quadratic functional. Ann. Statist. 33 2930-2956. MR2253108
    • (2005) Ann. Statist , vol.33 , pp. 2930-2956
    • Cai, T.1    Low, M.2
  • 10
    • 33644903538 scopus 로고    scopus 로고
    • Adaptive confidence balls
    • MR2275240
    • Cai, T. and Low, M. (2006a). Adaptive confidence balls. Ann. Statist. 34 202-228. MR2275240
    • (2006) Ann. Statist , vol.34 , pp. 202-228
    • Cai, T.1    Low, M.2
  • 11
    • 33644888851 scopus 로고    scopus 로고
    • Optimal adaptive estimation of a quadratic functional
    • MR2291501
    • Cai, T.andLow, M. (2006b). Optimal adaptive estimation of a quadratic functional. Ann. Statist. 34 2298-2325. MR2291501
    • (2006) Ann. Statist , vol.34 , pp. 2298-2325
    • Cai, T.1    Low, M.2
  • 12
    • 54349089152 scopus 로고    scopus 로고
    • Adaptive variance function estimation in heteroscedastic nonparametric regression
    • MR2458178
    • Cai, T.andWang, L. (2008). Adaptive variance function estimation in heteroscedastic nonparametric regression. Ann. Statist. 36 2025-2054. MR2458178
    • (2008) Ann. Statist , vol.36 , pp. 2025-2054
    • Cai, T.1    Wang, L.2
  • 14
    • 65349108741 scopus 로고    scopus 로고
    • A data-driven block thresholding approach to wavelet estimation
    • Cai, T.T.andZhou, H. H. (2009). A data-driven block thresholding approach to wavelet estimation. Ann. Statist. 87 569-595.
    • (2009) Ann. Statist , vol.87 , pp. 569-595
    • Cai, T.T.1    Zhou, H.H.2
  • 16
    • 28644439974 scopus 로고    scopus 로고
    • Asymptotic equivalence for a null recurrent diffusion
    • MR1895888
    • Delattre, S. and Hoffmann, M. (2002). Asymptotic equivalence for a null recurrent diffusion. Bernoulli 8 139-174. MR1895888
    • (2002) Bernoulli , vol.8 , pp. 139-174
    • Delattre, S.1    Hoffmann, M.2
  • 17
    • 84966241361 scopus 로고
    • Interpolation of Besov spaces
    • MR0920166
    • DeVore, R. and Popov, V. (1988). Interpolation of Besov spaces. Trans. Amer. Math. Soc. 305 397-414. MR0920166
    • (1988) Trans. Amer. Math. Soc , vol.305 , pp. 397-414
    • Devore, R.1    Popov, V.2
  • 18
    • 84950459514 scopus 로고
    • Adapting to unknown smoothness via wavelet shrinkage
    • MR1379464
    • Donoho, D.L. and Johnstone, I. M. (1995). Adapting to unknown smoothness via wavelet shrinkage. J. Amer. Statist. Assoc. 90 1200-1224. MR1379464
    • (1995) J. Amer. Statist. Assoc , vol.90 , pp. 1200-1224
    • Donoho, D.L.1    Johnstone, I.M.2
  • 19
    • 0032334093 scopus 로고    scopus 로고
    • Minimax estimation via wavelet shrinkage
    • MR1635414
    • Donoho, D.L. and Johnstone, I. M. (1998). Minimax estimation via wavelet shrinkage. Ann. Statist. 26 879-921. MR1635414
    • (1998) Ann. Statist , vol.26 , pp. 879-921
    • Donoho, D.L.1    Johnstone, I.M.2
  • 21
    • 38249016845 scopus 로고
    • Minimax quadratic estimation of a quadratic functional
    • MR1081043
    • Donoho, D.L. and Nussbaum, M. (1990). Minimax quadratic estimation of a quadratic functional. J. Complexity 6 290-323. MR1081043
    • (1990) J. Complexity , vol.6 , pp. 290-323
    • Donoho, D.L.1    Nussbaum, M.2
  • 22
    • 0040040083 scopus 로고    scopus 로고
    • New goodness-of-fit tests and their application to nonparametric confidence sets
    • MR1611768
    • Dümbgen, L. (1998). New goodness-of-fit tests and their application to nonparametric confidence sets. Ann. Statist. 26 288-314. MR1611768
    • (1998) Ann. Statist , vol.26 , pp. 288-314
    • Dümbgen, L.1
  • 23
    • 0030503140 scopus 로고    scopus 로고
    • On optimal adaptive estimation of a quadratic functional
    • MR1401840
    • Efromovich, S. Y. and Low, M. (1996). On optimal adaptive estimation of a quadratic functional. Ann. Statist. 24 1106-1125. MR1401840
    • (1996) Ann. Statist , vol.24 , pp. 1106-1125
    • Efromovich, S.Y.1    Low, M.2
  • 24
    • 0001097057 scopus 로고
    • On the estimation of quadratic functionals
    • MR1126325
    • Fan, J. (1991). On the estimation of quadratic functionals. Ann. Statist. 19 1273-1294. MR1126325
    • (1991) Ann. Statist , vol.19 , pp. 1273-1294
    • Fan, J.1
  • 25
    • 0036054269 scopus 로고    scopus 로고
    • Asymptotic equivalence of estimating a Poisson intensity and a positive diffusion drift
    • MR1922540
    • Genon-Catalot, V., Laredo, C. and Nussbaum, M. (2002). Asymptotic equivalence of estimating a Poisson intensity and a positive diffusion drift. Ann. Statist. 30 731-753. MR1922540
    • (2002) Ann. Statist , vol.30 , pp. 731-753
    • Genon-Catalot, V.1    Laredo, C.2    Nussbaum, M.3
  • 26
    • 22944431500 scopus 로고    scopus 로고
    • Confidence sets for nonparametric wavelet regression
    • MR2163157
    • Genovese, C. R. and Wasserman, L. (2005). Confidence sets for nonparametric wavelet regression. Ann. Statist. 33 698-729. MR2163157
    • (2005) Ann. Statist , vol.33 , pp. 698-729
    • Genovese, C.R.1    Wasserman, L.2
  • 27
    • 0032094580 scopus 로고    scopus 로고
    • Asymptotic equivalence for nonparametric generalized linear models
    • MR1633574
    • Grama, I. and Nussbaum, M. (1998). Asymptotic equivalence for nonparametric generalized linear models. Probab. Theory Related Fields 111 167-214. MR1633574
    • (1998) Probab. Theory Related Fields , vol.111 , pp. 167-214
    • Grama, I.1    Nussbaum, M.2
  • 28
    • 28644443022 scopus 로고    scopus 로고
    • Asymptotic equivalence for nonparametric regression
    • MR1900972
    • Grama, I.andNussbaum, M. (2002). Asymptotic equivalence for nonparametric regression. Math. Methods Statist. 11 1-36. MR1900972
    • (2002) Math. Methods Statist , vol.11 , pp. 1-36
    • Grama, I.1    Nussbaum, M.2
  • 29
    • 70049118696 scopus 로고    scopus 로고
    • Asymptotic equivalence of spectral density estimation and Gaussian white noise
    • Golubev, G. K., Nussbaum, M. and Zhou, H. H. (2009). Asymptotic equivalence of spectral density estimation and Gaussian white noise. Ann. Statist. To appear.
    • (2009) Ann. Statist. to Appear
    • Golubev, G.K.1    Nussbaum, M.2    Zhou, H.H.3
  • 31
    • 18444410406 scopus 로고    scopus 로고
    • Empirical Bayes selection of wavelet thresholds
    • MR2166560
    • Johnstone, I. M. and Silverman, B. W. (2005). Empirical Bayes selection of wavelet thresholds. Ann. Statist. 33 1700-1752. MR2166560
    • (2005) Ann. Statist , vol.33 , pp. 1700-1752
    • Johnstone, I.M.1    Silverman, B.W.2
  • 32
    • 32044439119 scopus 로고    scopus 로고
    • Sharp adaptive estimation of quadratic functionals
    • MR2214904
    • Klemelä, J. (2006). Sharp adaptive estimation of quadratic functionals. Probab. Theory Related Fields 134 539-564. MR2214904
    • (2006) Probab. Theory Related Fields , vol.134 , pp. 539-564
    • Klemelä, J.1
  • 33
    • 0000411204 scopus 로고
    • An approximation of partial sums of independent rv's and the sample df. i
    • MR0375412
    • Komlos, J., Major, P. and Tusnády, G. (1975). An approximation of partial sums of independent rv's and the sample df. I. Z. Wahrsch. Verw. Gebiete 32 111-131. MR0375412
    • (1975) Z. Wahrsch. Verw. Gebiete , vol.32 , pp. 111-131
    • Komlos, J.1    Major, P.2    Tusnády, G.3
  • 34
    • 0000524793 scopus 로고
    • Exact asymptotically minimax estimator for nonparametric regression in uniform norm
    • MR1318004
    • Korostelev, A. P. (1993). Exact asymptotically minimax estimator for nonparametric regression in uniform norm. Theory Probab. Appl. 38 775-782. MR1318004
    • (1993) Theory Probab. Appl , vol.38 , pp. 775-782
    • Korostelev, A.P.1
  • 35
    • 0034287154 scopus 로고    scopus 로고
    • Adaptive estimation of a quadratic functional by model selection
    • MR1805785
    • Laurent, B.andMassart, P. (2000). Adaptive estimation of a quadratic functional by model selection. Ann. Statist. 28 1302-1338. MR1805785
    • (2000) Ann. Statist , vol.28 , pp. 1302-1338
    • Laurent, B.1    Massart, P.2
  • 36
    • 0000457130 scopus 로고
    • Sufficiency and approximate sufficiency
    • MR0207093
    • Le Cam, L. (1964). Sufficiency and approximate sufficiency. Ann. Math. Statist. 35 1419-1455. MR0207093
    • (1964) Ann. Math. Statist , vol.35 , pp. 1419-1455
    • Le Cam, L.1
  • 38
    • 0000012624 scopus 로고
    • On a problem of adaptive estimation in white Gaussian noise
    • MR1091202
    • Lepski, O. V. (1990). On a problem of adaptive estimation in white Gaussian noise. Theory Probab. Appl. 35 454-466. MR1091202
    • (1990) Theory Probab. Appl , vol.35 , pp. 454-466
    • Lepski, O.V.1
  • 39
    • 0040276000 scopus 로고
    • Honest confidence regions for nonparametric regression
    • MR1015135
    • Li, K.-C. (1989). Honest confidence regions for nonparametric regression. Ann. Statist. 17 1001-1008. MR1015135
    • (1989) Ann. Statist , vol.17 , pp. 1001-1008
    • Li, K.-C.1
  • 40
    • 0004198869 scopus 로고
    • Cambridge Univ. Press, Cambridge. MR1228209
    • Meyer, Y. (1992). Wavelets and Operators. Cambridge Univ. Press, Cambridge. MR1228209
    • (1992) Wavelets and Operators
    • Meyer, Y.1
  • 41
    • 0032263667 scopus 로고    scopus 로고
    • Diffusion approximation for nonparametric autoregression
    • MR1664703
    • Milstein, G. and Nussbaum, M. (1998). Diffusion approximation for nonparametric autoregression. Probab. Theory Related Fields 112 535-543. MR1664703
    • (1998) Probab. Theory Related Fields , vol.112 , pp. 535-543
    • Milstein, G.1    Nussbaum, M.2
  • 42
    • 0030328670 scopus 로고    scopus 로고
    • Asymptotic equivalence of density estimation and Gaussian white noise
    • MR1425959
    • Nussbaum, M. (1996). Asymptotic equivalence of density estimation and Gaussian white noise. Ann. Statist. 24 2399-2430. MR1425959
    • (1996) Ann. Statist , vol.24 , pp. 2399-2430
    • Nussbaum, M.1
  • 43
    • 0000056062 scopus 로고
    • Optimal filtering of square integrable signals in Gaussian white noise
    • Pinsker, M. S. (1980). Optimal filtering of square integrable signals in Gaussian white noise. Problems Inform. Transmission 120-133.
    • (1980) Problems Inform. Transmission , pp. 120-133
    • Pinsker, M.S.1
  • 44
    • 0000315855 scopus 로고    scopus 로고
    • Adaptive and spatially adaptive testing of nonparametric hypothesis
    • MR1651777
    • Spokoiny, V. G. (1998). Adaptive and spatially adaptive testing of nonparametric hypothesis. Math. Methods Statist. 7 245-273. MR1651777
    • (1998) Math. Methods Statist , vol.7 , pp. 245-273
    • Spokoiny, V.G.1
  • 45
    • 0024921922 scopus 로고
    • Wavelet and dilation equations: A brief introduction
    • MR1025484
    • Strang, G. (1992). Wavelet and dilation equations: A brief introduction. SIAM Rev. 31 614-627. MR1025484
    • (1992) SIAM Rev , vol.31 , pp. 614-627
    • Strang, G.1
  • 48
    • 0036051612 scopus 로고    scopus 로고
    • Asymptotic nonequivalence of GARCH models and diffusions
    • MR1922541
    • Wang, Y. Z. (2002). Asymptotic nonequivalence of GARCH models and diffusions. Ann. Statist. 30 754-783. MR1922541
    • (2002) Ann. Statist , vol.30 , pp. 754-783
    • Wang, Y.Z.1
  • 49
    • 18444396908 scopus 로고    scopus 로고
    • General empirical Bayes wavelet methods and exactly adaptive minimax estimation
    • MR2157796
    • Zhang, C.-H. (2005). General empirical Bayes wavelet methods and exactly adaptive minimax estimation. Ann. Statist. 33 54-100. MR2157796
    • (2005) Ann. Statist , vol.33 , pp. 54-100
    • Zhang, C.-H.1
  • 50
    • 70049112134 scopus 로고    scopus 로고
    • A note on quantile coupling inequalities and their applications Available at
    • Zhou, H. H. (2006). A note on quantile coupling inequalities and their applications. Available at http://www.stat.yale.edu/~hz68.
    • (2006)
    • Zhou, H.H.1


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