Heteroscedasticity checks for single index models

被引:7
|
作者
Zhu, Xuehu [1 ,2 ]
Guo, Xu [1 ,3 ]
Lin, Lu [2 ]
Zhu, Lixing [1 ]
机构
[1] Hong Kong Baptist Univ, Hong Kong, Hong Kong, Peoples R China
[2] Shandong Univ, Jinan 250100, Peoples R China
[3] Nanjing Univ Aeronaut & Astronaut, Nanjing, Jiangsu, Peoples R China
关键词
Heteroscedasticity check; Single index model; Nonparametric estimation; Dimension reduction; DIMENSION REDUCTION; TESTING HETEROSCEDASTICITY; VARIANCE FUNCTION; PARAMETRIC FORM; REGRESSION;
D O I
10.1016/j.jmva.2015.01.007
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
To test heteroscedasticity in single index models, in this paper two test statistics are proposed via quadratic conditional moments. Without the use of dimension reduction structure, the first test has the usual convergence rate in nonparametric sense. Under the dimension reduction structure of mean and variance functions, the second one has faster convergence rate to its limit under the null hypothesis, and can detect local alternative hypotheses distinct from the null at a much faster rate than the one the first test can achieve. Numerical studies are also carried out to evaluate the performance of the developed tests. Interestingly, the second one works much better than the first one if the variance function does have a dimension reduction structure. However, it is not robust against the violation of dimension reduction structure, in other words, the power performance of the second test may not be encouraging if without the dimension reduction structure. (C) 2015 Elsevier Inc. All rights reserved.
引用
收藏
页码:41 / 55
页数:15
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