Wavelet based estimation for the derivative of a density by block thresholding under random censorship

Abstract

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 Hall and Patil (1995) for density estimation in the complete data case that has been extended recently by Li (2003Li ( , 2008. We find bounds for the L 2 -loss over a large range of Besov function classes for the resulting estimators. The results of Patil (1995), Prakasa Rao (1996) and Li (2003Li ( , 2008 are obtained as special cases and the performance of proposed estimator is investigated by numerical study.

Nonparametric estimation of a quantile density function by wavelet methods

“…The new smooth linear wavelet estimator has been adapted from [17,18]. [1,2], [9,10] and [42,43] have proposed this version of wavelet estimators Estimation of quantile density GLD(0,7,7,7),n=200 Matlab which are adapted from [36]. We compare these three estimators withĝ j1 (x) andĝ S (x), two estimators given in (1.4) and (1.6), respectively.…”