Testing conditional moment restrictions

• 成果类型: Article
• 署名作者: Tripathi, G; Kitamura, Y
• 署名单位: University of Wisconsin System; University of Wisconsin Madison; University of Pennsylvania
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 2003
• 页码: 2059-2095
• 关键词: empirical likelihood; functional form; semiparametric regression; estimating equations; specification; models; EFFICIENCY; estimator; GOODNESS; fit

摘要

Let (x,z) be a pair of observable random vectors. We construct a new smoothed empirical likelihood-based test for the hypothesis E{g(z, theta) \x} = 0 w.p. 1, where g is a vector of known functions and theta an unknown finite-dimensional parameter. We show that the test statistic is asymptotically normal under the null hypothesis and derive its asymptotic distribution under a sequence of local alternatives. Furthermore, the test is shown to possess an optimality property in large samples. Simulation evidence suggests that it also behaves well in small samples.