ASYMPTOTIC DISTRIBUTION-FREE TESTS FOR SEMIPARAMETRIC REGRESSIONS WITH DEPENDENT DATA

• 成果类型: Article
• 署名作者: Escanciano, Juan Carlos; Carlos Pardo-Fernandez, Juan; Van Keilegom, Ingrid
• 署名单位: Indiana University System; Indiana University Bloomington; Universidade de Vigo; KU Leuven
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/17-AOS1581
• 发表日期: 2018
• 页码: 1167-1196
• 关键词: of-fit tests; nonparametric model checks; parametric regression; UNIFORM-CONVERGENCE; variance; MARKET; RISK; estimators; return; rates

摘要

This article proposes a new general methodology for constructing nonparametric and semiparametric Asymptotically Distribution-Free (ADF) tests for semiparametric hypotheses in regression models for possibly dependent data coming from a strictly stationary process. Classical tests based on the difference between the estimated distributions of the restricted and unrestricted regression errors are not ADF. In this article, we introduce a novel transformation of this difference that leads to ADF tests with well-known critical values. The general methodology is illustrated with applications to testing for parametric models against nonparametric or semiparametric alternatives, and semiparametric constrained mean-variance models. Several Monte Carlo studies and an empirical application show that the finite sample performance of the proposed tests is satisfactory in moderate sample sizes.