scholarly journals A Berry-Esseen Type Bound in Kernel Density Estimation for Negatively Associated Censored Data

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Qunying Wu ◽  
Pingyan Chen
Keyword(s):  
Fixed Point ◽  
Censored Data ◽  
Kernel Estimation ◽  
Kernel Density ◽  
Kernel Density Estimator ◽  
Regularity Conditions ◽  
Density Estimator ◽  
Negatively Associated ◽  
Kaplan Meier ◽  
Na Sequences

We discuss the kernel estimation of a density function based on censored data when the survival and the censoring times form the stationary negatively associated (NA) sequences. Under certain regularity conditions, the Berry-Esseen type bounds are derived for the kernel density estimator and the Kaplan-Meier kernel density estimator at a fixed pointx.

scholarly journals Smooth Kernel Estimation of a Circular Density Function: A Connection to Orthogonal Polynomials on the Unit Circle

2018 ◽  
Vol 2018 ◽  
pp. 1-4 ◽  
Author(s):  
Yogendra P. Chaubey
Keyword(s):  
Orthogonal Polynomials ◽  
Unit Circle ◽  
Kernel Estimation ◽  
Kernel Density ◽  
Cauchy Distribution ◽  
Kernel Density Estimator ◽  
Circular Statistics ◽  
Cauchy Kernel ◽  
Density Estimator

The circular kernel density estimator, with the wrapped Cauchy kernel, is derived from the empirical version of Carathéodory function that is used in the literature on orthogonal polynomials on the unit circle. An equivalence between the resulting circular kernel density estimator, to Fourier series density estimator, has also been established. This adds further weight to the considerable role of the wrapped Cauchy distribution in circular statistics.

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