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Nonparametric regression estimates with censored data based on block thresholding method. (English) Zbl 1432.62108
Summary: Here we consider wavelet-based identification and estimation of a censored nonparametric regression model via block thresholding methods and investigate their asymptotic convergence rates. We show that these estimators, based on block thresholding of empirical wavelet coefficients, achieve optimal convergence rates over a large range of Besov function classes, and in particular enjoy those rates without the extraneous logarithmic penalties that are usually suffered by term-by-term thresholding methods. This work is extension of results in [L. Li et al., “On the optimality of wavelet-based nonparametric regression with censored data”, J. Appl. Probab. Stat. 3, No. 2, 243–261 (2008)]. The performance of proposed estimator is investigated by a numerical study.

MSC:
62G08 Nonparametric regression and quantile regression
62G07 Density estimation
62G20 Asymptotic properties of nonparametric inference
62-08 Computational methods for problems pertaining to statistics
Software:
WaveLab; wavethresh
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