半参数回归模型的异方差统计分析

基金项目:

国家自然科学基金资助项目(10371042)和上海科委重点资助项目(02DJ14063).

详细信息

Statistical Analysis of Heteroscedasticity in Semiparametric Models

摘要: 在回归分析中,方差齐性的假设是一个普遍关心的问题.在参数和非参数回归模型中,关于异方差检验问题已经有很多的研究,见([1],[4],[7]).本文研究了半参数回归模型的异方差检验问题,得到了方差齐性检验的SCORE统计量,证明了该统计量的渐近x²性质,最后给出计算机模拟和实际例子,推广和发展了Eubank和Thomas(1993),韦博成(1995)的工作.
- 异方差 /
- 半参数回归 /
- Score检验
Abstract: The assumption of homoscedasticity is commonly concerned in regression analysis. In parametric and nonparametric regression models, the problem of testing of heteroscedasticity was discussed by Cook ＆ wesiberg （1983）, Eubank ＆ Thomas （1993） and Wei （1995）. In this paper, the testing of heteroscedasticity is researched for semiparametric regression model. The score test is obtained to test hypothesis of homoscedasticity and the asymptotic chi-squared property under the null hypothesis is proved. Simulations are done and we illustrate our test methods by using the mouthwash data （Speckman, P. （1988））.