Random rates in anisotropic regression (with a discussion and a rejoinder by the authors)

[1]  W. Härdle,et al.  Optimal Bandwidth Selection in Nonparametric Regression Function Estimation , 1985 .

[2]  Ion Grama,et al.  Asymptotic equivalence for nonparametric generalized linear models , 1998 .

[3]  D. Picard,et al.  Adaptive confidence interval for pointwise curve estimation , 2000 .

[4]  Yi Lin.  Tensor product space ANOVA models , 2000 .

[5]  C. J. Stone,et al.  The Dimensionality Reduction Principle for Generalized Additive Models , 1986 .

[6]  A. Tsybakov,et al.  Optimal aggregation of classifiers in statistical learning , 2003 .

[7]  O. Lepski,et al.  Adaptive non-parametric estimation of smooth multivariate functions , 1999 .

[8]  Lianfen Qian,et al.  Nonparametric Curve Estimation: Methods, Theory, and Applications , 1999, Technometrics.

[9]  V. Spokoiny,et al.  Optimal pointwise adaptive methods in nonparametric estimation , 1997 .

[10]  O. Lepskii.  On a Problem of Adaptive Estimation in Gaussian White Noise , 1991 .

[11]  H. Chernoff.  LARGE-SAMPLE THEORY: PARAMETRIC CASE' , 1956 .

[12]  Julian J. Faraway.  Bootstrap selection of bandwidth and confidence bands for nonparametric regression , 1990 .

[13]  V. Spokoiny,et al.  Multiscale testing of qualitative hypotheses , 2001 .

[14]  P. Massart,et al.  Risk bounds for model selection via penalization , 1999 .

[15]  A. Tsybakov,et al.  Sharp adaptation for inverse problems with random noise , 2002 .

[16]  S. Efroimovich.  Nonparametric Estimation of a Density of Unknown Smoothness , 1986 .

[17]  A. Juditsky,et al.  On Minimax Wavelet Estimators , 1996 .

[18]  Dominique Picard,et al.  A note on the wavelet oracle , 1999 .

[19]  I. Johnstone,et al.  Ideal spatial adaptation by wavelet shrinkage , 1994 .

[20]  Imre Csiszár,et al.  Information Theory - Coding Theorems for Discrete Memoryless Systems, Second Edition , 2011 .

[21]  Rainer von Sachs,et al.  Wavelet thresholding in anisotropic function classes and application to adaptive estimation of evolutionary spectra , 1997 .

[22]  Alfréd Rényi,et al.  On the theory of random search , 1965 .

[23]  L. Brown,et al.  Asymptotic equivalence of nonparametric regression and white noise , 1996 .

[24]  A. Tsybakov,et al.  Introduction à l'estimation non-paramétrique , 2003 .

[25]  M. Nikolskii,et al.  Approximation of Functions of Several Variables and Embedding Theorems , 1971 .

[26]  Ker-Chau Li,et al.  Honest Confidence Regions for Nonparametric Regression , 1989 .

[27]  A. Tsybakov,et al.  Oracle inequalities for inverse problems , 2002 .

[28]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[29]  P. Hall.  EFFECT OF BIAS ESTIMATION ON COVERAGE ACCURACY OF BOOTSTRAP CONFIDENCE INTERVALS FOR A PROBABILITY DENSITY , 1992 .

[30]  I. I. Tsitovich,et al.  SEQUENTIAL SEARCH FOR SIGNIFICANT VARIABLES OF AN UNKNOWN FUNCTION , 1997 .

[31]  P. Hall,et al.  Block threshold rules for curve estimation using kernel and wavelet methods , 1998 .

[32]  G. Kerkyacharian,et al.  Nonlinear estimation in anisotropic multi-index denoising , 2001 .

[33]  G. Wahba.  Spline models for observational data , 1990 .

[34]  V. V. Petrov.  Sums of Independent Random Variables , 1975 .

[35]  M. Nussbaum.  Asymptotic Equivalence of Density Estimation and Gaussian White Noise , 1996 .

[36]  Lawrence D. Brown,et al.  Superefficiency in Nonparametric Function Estimation , 1997 .

[37]  R. Z. Khasʹminskiĭ,et al.  Statistical estimation : asymptotic theory , 1981 .

[38]  Alexander Goldenshluger,et al.  Adaptive Prediction and Estimation in Linear Regression with Infinitely Many Parameters , 2001 .

[39]  G. Wahba,et al.  Smoothing spline ANOVA for exponential families, with application to the Wisconsin Epidemiological Study of Diabetic Retinopathy : the 1994 Neyman Memorial Lecture , 1995 .

[40]  Michael H. Neumann.  Automatic bandwidth choice and confidence intervals in nonparametric regression , 1995 .

[41]  E. Mammen,et al.  Optimal spatial adaptation to inhomogeneous smoothness: an approach based on kernel estimates with variable bandwidth selectors , 1997 .

[42]  P. Hall.  Edgeworth expansions for nonparametric density estimators, with applications , 1991 .

[43]  J. Polzehl,et al.  Image denoising: Pointwise adaptive approach , 2003 .

[44]  Mark G. Low.  On nonparametric confidence intervals , 1997 .

[45]  O. Lepskii,et al.  On problems of adaptive estimation in white Gaussian noise , 1992 .