A strong consistency of a nonparametric estimate of entropy under random censorship

New Entropy Estimator with an Application to Test of Normality

“…Remark 4.3 The main problem in using entropy estimates such as in (1.5) is to choose properly the smoothing parameter h n . With a lot more effort, we could derive analog results here for H ε;n (X) using the methods in Bouzebda and Elhattab (2009, 2010, 2011, as well as the modern empirical process tools developed in Einmahl and Mason (2005) in their work on uniform in bandwidth consistency of kernel-type estimators.…”

Kernel Estimation of Entropy Function for Length-Biased Censored Data

“…For a detailed review work of different nonparametric estimators of Shannon entropy, one can refer to Beirlant et al (1997). Nonparametric estimation of entropy under random censoring was studied by Carbonez et al (1991) and Bouzebda and Elhattab (2009) respectively, in which the former proposed to estimate entropy using histogram density estimate and the latter with kernel density estimate. Both studied the strong consistency of the entropy estimate under suitable regularity conditions.…”

Nonparametric Recursive Method for Kernel-Type Function Estimators for Censored Data

“…It is worth noticing that the bandwidth selection methods studied in the literature can be divided into three broad classes: the cross-validation techniques, the plug-in ideas and the bootstrap. Recently, some general methods based upon empirical process techniques are developed in order to prove uniform in bandwidth consistency of a class of kernel-type function estimators (density, regression, entropy and copula), we may refer to [23,24], [5,6], [4], [7] and [8]. Further, recursive kernel density estimators defined by stochastic approximation method have been proposed by [41], recursive kernel distribution estimators have been done by [42], recursive regression estimators have been done by [43,44] and recursive kernel-type estimators for spatial data was proposed by [9,10,11,12].…”