Data driven smooth tests for composite hypotheses

• 成果类型: Article
• 署名作者: Inglot, T; Kallenberg, WCM; Ledwina, T
• 署名单位: Wroclaw University of Science & Technology; University of Twente
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1997
• 页码: 1222-1250
• 关键词: GOODNESS-OF-FIT; location-scale families; asymptotic power; cramer-vonmises; UNIFORMITY; version; models

摘要

The classical problem of testing goodness-of-fit of a parametric family is reconsidered. A new test for this problem is proposed and investigated. The new test statistic is a combination of the smooth test statistic and Schwarz's selection rule. More precisely, as the sample size increases, an increasing family of exponential models describing departures from the null model is introduced and Schwarz's selection rule is presented to select among them. Schwarz's rule provides the right dimension given by the data, while the smooth test in the right dimension finishes the job. Theoretical properties of the selection rules are derived under null and alternative hypotheses. They imply consistency of data driven smooth tests for composite hypotheses at essentially any alternative.