Wavelet-based quantile density function estimation under random censorship

In this paper, the estimation of a quantile density function in the presence of right censored data is investigated. A new wavelet-based methodology for the estimation of the quantile function will is proposed. In particular, an adaptive hard thresholding wavelet estimator is constructed. Under mild assumptions on the model, we prove that it enjoys powerful mean integrated squared error properties over Besov balls. While existing estimators of the quantile density function are not good at the tails, our proposed estimators perform well at the tails. The comparison of the proposed estimator has been made with estimators given by Jones (1992) Ann Inst Stat Math 44(4):721–727 and Soni et al. (2012) Comput Stat Data Anal 56(12):3876–3886 graphically and in terms of the mean integrated square error (MISE) for the uncensored case.