Testing for additivity with B-splines

被引：0

作者：

Hengjian CUI Xuming HE Li LIU Department of Statistics and Financial Mathematics School of Mathematical Sciences Beijing Normal University Beijing China ^{[100875
]}

Department of Statistics University of Illinois Champaign IL USA ^{[61820
]}

National Institute of Statistical Science Durham NC USA ^{[27709
]}

机构：

来源：

Science in China(Series A:Mathematics) | 2007年 / 06期

关键词：

additivity; B-splines; dimension reduction; score test; smoothing; Tukey test;

D O I：

暂无

中图分类号：

O212.7 [非参数统计];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

<正>Regression splines are often used for fitting nonparametric functions, and they work especially well for additivity models. In this paper, we consider two simple tests of additivity: an adaptation of Tukey's one degree of freedom test and a nonparametric version of Rao's score test. While the Tukey-type test can detect most forms of the local non-additivity at the parametric rate of O(n-1/2), the score test is consistent for all alternative at a nonparametric rate. The asymptotic distribution of these test statistics is derived under both the null and local alternative hypotheses. A simulation study is conducted to compare their finite-sample performances with some existing kernel-based tests. The score test is found to have a good overall performance.

引用

页码：841 / 858

页数：18