LARGE SAMPLE STUDY OF EMPIRICAL DISTRIBUTIONS IN A RANDOM-MULTIPLICATIVE CENSORING MODEL

• 成果类型: Article
• 署名作者: VARDI, Y; ZHANG, CH
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176348668
• 发表日期: 1992
• 页码: 1022-1039
• 关键词: MAXIMUM-LIKELIHOOD ESTIMATORS

摘要

Consider an incomplete data problem with the following specifications. There are three independent samples (X1,..., X(m)), (Z1,..., Z(n)) and (U1,..., U(n)). The first two samples are drawn from a common lifetime distribution function G, while the third sample is drawn from the uniform distribution over the interval (0, 1). In this paper we derive the large sample properties of G(m,n), the nonparametric maximum likelihood estimate of G based on the observed data X1,..., X(m) and Y1,..., Y(n), where Y(i) = Z(i)U(i), i = 1,..., n. (The Z's and U's are unobservable.) In particular we show that if m and n approach infinity at a suitable rate, then sup(t)\G(m,n)(t) - G(t)\ --> 0 (a.s.), square-root m + n (G(m,n) - G) converges weakly to a Gaussian process and the estimate G(m,n) is asymptotically efficient in a nonparametric sense.