HELLINGER-CONSISTENCY OF CERTAIN NONPARAMETRIC MAXIMUM-LIKELIHOOD ESTIMATORS

• 成果类型: Article
• 署名作者: VANDEGEER, S
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176349013
• 发表日期: 1993
• 页码: 14-44
• 关键词: Empirical Processes

摘要

Consider a class P = {P(theta) : theta is-an-element-of THETA} of probability measures on a measurable space (K, A), dominated by a sigma-finite measure mu. Let f(theta) = dP(theta)/dmu, theta is-an-element-of THETA, and let theta(n) be a maximum likelihood estimator based on n independent observations from P(theta0), theta0 is-an-element-of THETA). We use results from empirical process theory to obtain convergence for the Hellinger distance h(f(thetan), f(theta0)), under certain entropy conditions on the class of densities {f(theta) : theta is-an-element-of THETA}. The examples we present are a model with interval censored observations, smooth densities, monotone densities and convolution models. In most examples, the convexity of the class of densities is of special importance.