Approximate and asymptotic distributions of chi-squared-type mixtures with applications

• 成果类型: Article
• 署名作者: Zhang, JT
• 署名单位: National University of Singapore
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/016214504000000575
• 发表日期: 2005
• 页码: 273-285
• 关键词: GOODNESS-OF-FIT; Nonparametric Regression; checking; models

摘要

In this article we study how to approximate a random variable T of general chi-squared-type mixtures by a random variable of the form alpha chi(2)(d) + beta via matching the first three cumulants. The approximation error bounds for the density functions of the chi-squared approximation and the normal approximation are established. Applications of the results to some nonparametric goodness-of-fit tests, including those tests based on orthogonal series, smoothing splines, and local polynomial smoothers, are investigated. Two simulation studies are conducted to compare the chi-squared approximation and the normal approximation numerically. The chi-squared approximation is illustrated using a real data example for polynomial goodness-of-fit tests.