Nonparametric estimation of a distribution subject to a stochastic precedence constraint

• 成果类型: Article
• 署名作者: Arcones, MA; Kvam, PH; Samaniego, FJ
• 署名单位: State University of New York (SUNY) System; Binghamton University, SUNY; University System of Georgia; Georgia Institute of Technology; University of California System; University of California Davis
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/016214502753479310
• 发表日期: 2002
• 页码: 170-182
• 关键词: maximum-likelihood-estimation; redundancy allocations; survival-curve

摘要

For any two random variables X and Y with distributions F and G defined on [0, infinity), X is said to stochastically precede I' if P(X less than or equal to Y) greater than or equal to 1/2. For independent X and 1, stochastic precedence (denoted by X less than or equal to(sp) Y) is equivalent to E[G(X-)] less than or equal to 1/2. The applicability of stochastic precedence in various statistical contexts, including reliability modeling, tests for distributional equality versus various alternatives, and the relative performance of comparable tolerance bounds, is discussed. The problem of estimating the underlying distribution(s) of experimental data under the assumption that they obey a stochastic precedence (sp) constraint is treated in detail. Two estimation approaches, one based on data shrinkage and the other involving data translation, are used to construct estimators that conform to the sp constraint, and each is shown to lead to a root n-consistent estimator of the underlying distribution. The asymptotic behavior of each of the estimators is fully characterized. Conditions are given under which each estimator is asymptotically equivalent to the corresponding empirical distribution function or, in the case of right censoring, the Kaplan-Meier estimator. In the complementary cases, evidence is presented, both analytically and via simulation, demonstrating that the new estimators tend to outperform the empirical distribution function when sample sizes are sufficiently large.