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Wavelet based estimation for the derivative of a density by block thresholding under random censorship. (English) Zbl 1296.62187
Summary: We consider wavelet based method for estimating derivatives of a density via block thresholding when the data obtained are randomly right censored. The proposed method is analogous to that of P. Hall and P. Patil [Ann. Stat. 23, No. 3, 905–928 (1995; Zbl 0839.62042)] for density estimation in the complete data case that has been extended recently by L. Li [J. Stat. Plann. Inference 117, No. 1, 35–58 (2003; Zbl 1022.62038); J. Multivariate Anal. 99, No. 8, 1518–1543 (2008; Zbl 1144.62026)]. We find bounds for the \(L_{2}\)-loss over a large range of Besov function classes for the resulting estimators. The results of Hall and Patil [loc. cit.], B. L. S. Prakasa Rao [Bull. Inf. Cybern. 28, No. 1, 91–100 (1996; Zbl 0864.62023)] and Li [2003, 2008, loc. cit.] are obtained as special cases and the performance of the proposed estimator is investigated by a numerical study.

MSC:
62N02 Estimation in survival analysis and censored data
62G05 Nonparametric estimation
62G07 Density estimation
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