CENTRAL LIMIT-THEOREMS FOR LP DISTANCES OF KERNEL ESTIMATORS OF DENSITIES UNDER RANDOM CENSORSHIP

• 成果类型: Article
• 署名作者: CSORGO, M; GOMBAY, E; HORVATH, L
• 署名单位: University of Alberta; Utah System of Higher Education; University of Utah
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176348372
• 发表日期: 1991
• 页码: 1813-1831
• 关键词: strong approximations

摘要

A sequence of independent nonnegative random variables with common distribution function F is censored on the right by another sequence of independent identically distributed random variables. These two sequences are also assumed to be independent. We estimate the density function f of F by a sequence of kernel estimators f(n)(t) = (integral-infinity(infinity)K((t - x)/h(n)) dF(n)(x))/h(n), where h(n) is a sequence of numbers, K is kernel density function and F(n) is the product-limit estimator of F. We prove central limit theorems for integral 0T\f(n)(t) - f(t)\p d-mu(t), 1 less-than-or-equal-to p < infinity, 0 < T less-than-or-equal-to infinity, where mu is a measure on the Borel sets of the real line. The result is tested in Monte Carlo trials and applied for goodness of fit.