Exact Risk Analysis of Wavelet Regression

J. S. Marron; Süleyman Adak; Iain M. Johnstone; Michael H. Neumann; Pravin S. Patil

doi:10.1080/10618600.1998.10474777

Abstract

Abstract Wavelets have motivated development of a host of new ideas in nonparametric regression smoothing. Here we apply the too] of exact risk analysis, to understand the small sample behavior of wavelet estimators, and thus to check directly the conclusions suggested by asymptotics. Comparisons between some wavelet bases, and also between hard and soft thresholding, are given from several viewpoints. Our results provide insight as to why the viewpoints and conclusions of Donoho and Johnstone differ from those of Hall and Patil.

Keywords

WaveletViewpointsEstimatorMathematicsNonparametric regressionSmoothingRegressionStatisticsEconometricsNonparametric statisticsRegression analysisSample (material)Computer scienceArtificial intelligence

Affiliated Institutions

Related Publications

Regularization of Wavelets Approximations

Anestis Antoniadis , Jianqing Fan

this paper, weintroduce nonlinear regularized wavelet estimators for estimating nonparametric regression functions when sampling points are not uniformly spaced. The approach ca...

2011 eScholarship (California Digital Libr... 48 citations

Regularization of Wavelet Approximations

Anestis Antoniadis , Jianqing Fan

AbstractIn this paper, we introduce nonlinear regularized wavelet estimators for estimating nonparametric regression functions when sampling points are not uniformly spaced. The...

2001 Journal of the American Statistical A... 488 citations

WAVESHRINK WITH FIRM SHRINKAGE

Hong‐Ye Gao , A. Gregory Bruce

Abstract: Donoho and Johnstone’s (1994) WaveShrink procedure has proven valu-able for signal de-noising and non-parametric regression. WaveShrink has very broad asymptotic near-...

1997 277 citations

Ideal Spatial Adaptation by Wavelet Shrinkage

David L. Donoho , Iain M. Johnstone

Journal Article Ideal spatial adaptation by wavelet shrinkage Get access David L Donoho, David L Donoho Department of Statistics, Stanford University, Stanford, California, U.S....

1994 Biometrika 2460 citations

Component selection and smoothing in multivariate nonparametric regression

Yi Lin , Hao Helen Zhang

We propose a new method for model selection and model fitting in multivariate nonparametric regression models, in the framework of smoothing spline ANOVA. The “COSSO ” is a meth...

2006 The Annals of Statistics 563 citations

Publication Info

Year: 1998
Type: article
Volume: 7
Issue: 3
Pages: 278-309
Citations: 77
Access: Closed

External Links

View on DOI.org

Social Impact

Altmetric

Exact Risk Analysis of Wavelet Regression

PlumX Metrics

Social media, news, blog, policy document mentions

Citation Metrics

OpenAlex

Cite This

APA Style

                            
                                
                                    J. S. Marron, 
                                
                                    Süleyman Adak, 
                                
                                    Iain M. Johnstone
                                
                                et al.
                            
                            (1998). 
                            Exact Risk Analysis of Wavelet Regression. 
                            Journal of Computational and Graphical Statistics
                            , 7
                            (3)
                            , 278-309.
                            https://doi.org/10.1080/10618600.1998.10474777
                        

Identifiers

DOI: 10.1080/10618600.1998.10474777