期刊名称：Sankhya. Series A, mathematical statistics and probability
印刷版ISSN：0976-836X
电子版ISSN：0976-8378
出版年度：2011
卷号：73
期号：2
页码：231-244
DOI：10.1007/s13171-011-0016-y
语种：English
出版社：Indian Statistical Institute
摘要：We consider the problem of estimating the unknown response function and its derivatives in the standard nonparametric regression model. Recently, Abramovich et al. (2010) applied a Bayesian testimation procedure in a wavelet context and proved asymptotical minimaxity of the resulting adaptive level-wise maximum a posteriori wavelet testimator of the unknown response function and its derivatives in the Gaussian white noise model. Using the boundary-modified coiflets of Johnstone and Silverman (2004), we show that dicretization of the data does not affect the order of magnitude of the accuracy of a discrete version of the suggested level-wise maximum a posteriori wavelet testimator, obtaining thus its adaptivity and asymptotical minimaxity in the standard nonparametric regression model that is usually considered in practical applications. Simulated examples are used to illustrate the performance of the developed wavelet testimation procedure and compared with three recently proposed empirical Bayes wavelet estimators and a block thresholding wavelet estimator.
关键词：Adaptive estimation ; Besov spaces ; boundary wavelets ; coiflets ; Gaussian white noise model ; multiple testing ; nonparametric regression model ; thresholding ; wavelet analysis
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