ASYMPTOTICALLY OPTIMAL TESTS FOR CONDITIONAL DISTRIBUTIONS

• 成果类型: Article
• 署名作者: FALK, M; MAROHN, F
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176349014
• 发表日期: 1993
• 页码: 45-60
• 关键词: regression quantiles; kernel

摘要

Let (X1, Y1),..., (X(n), Y(n)) be independent replicates of the random vector (X, Y) is-an-element-of R(d+m), where X is R(d)-valued and Y is R(m)-valued. We assume that the conditional distribution P(Y is-an-element-of .\X = x) = Q(v)(.) of Y given X = x is a member of a parametric family, where the parameter space THETA is an open subset of R(k) with 0 is-an-element-of THETA. Under suitable regularity conditions we establish upper bounds for the power functions of asymptotic level-alpha tests for the problem v = 0 against a sequence of contiguous alternatives, as well as asymptotically optimal tests which attain these bounds. Since the testing problem involves the joint density of (X, Y) as an infinite dimensional nuisance parameter, its solution is not standard. A Monte Carlo simulation exemplifies the influence of this nuisance parameter. As a main tool we establish local asymptotic normality (LAN) of certain Poisson point processes which approximately describe our initial sample.