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Weak and strong uniform consistency rates of kernel density estimates for randomly censored data
Author(s) -
Karunamuni R. J.,
Yang Song
Publication year - 1991
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315426
Subject(s) - consistency (knowledge bases) , kernel density estimation , mathematics , statistics , kernel (algebra) , weak consistency , strong consistency , econometrics , statistical physics , combinatorics , physics , geometry , estimator
Let X 1 ,., X n , be i.i.d. random variables with distribution function F , and let Y 1 ,.,.,Y n be i.i.d. with distribution function G. For i = 1, 2,.,., n set δ i , = 1 if X i ≤ Y i , and 0 otherwise, and X i , = min{X i , K i }. A kernel‐type density estimate of f , the density function of F w.r.t. Lebesgue measure on the Borel o‐field, based on the censored data (δ i , X i ), i = 1,.,., n , is considered. Weak and strong uniform consistency properties over the whole real line are studied. Rates of convergence results are established under higher‐order differentiability assumption on f . A procedure for relaxing such assumptions is also proposed.