Heteroscedasticity checks for regression models
Zhu, LX; Fujikoshi, Y; Naito, K
AbstractFor checking on heteroscedasticity in regression models, a unified approach is proposed to constructing test statistics in parametric and nonparametric regression models. For nonparametric regression, the test is not affected sensitively by the choice of smoothing parameters which are involved in estimation of the nonparametric regression function. The limiting null distribution of the test statistic remains the same in a wide range of the smoothing parameters. When the covariate is one-dimensional, the tests are, under some conditions, asymptotically distribution-free. In the high-dimensional cases, the validity of bootstrap approximations is investigated. It is shown that a variant of the wild bootstrap is consistent while the classical bootstrap is not in the general case, but is applicable if some extra assumption on conditional variance of the squared error is imposed. A simulation study is performed to provide evidence of how the tests work and compare with tests that have appeared in the literature. The approach may readily be extended to handle partial linear, and linear autoregressive models.
Keywordbootstrap empirical process heteroscedasticity
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000172008800002
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Document Type期刊论文
Corresponding AuthorZhu, LX
Affiliation1.Chinese Acad Sci, Inst Appl Math, Acad Math & Syst Sci, Beijing 100080, Peoples R China
2.Univ Hong Kong, Dept Stat & Actuarial Sci, Hong Kong, Hong Kong, Peoples R China
3.Hiroshima Univ, Dept Math, Hiroshima 730, Japan
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GB/T 7714
Zhu, LX,Fujikoshi, Y,Naito, K. Heteroscedasticity checks for regression models[J]. SCIENCE IN CHINA SERIES A-MATHEMATICS PHYSICS ASTRONOMY,2001,44(10):1236-1252.
APA Zhu, LX,Fujikoshi, Y,&Naito, K.(2001).Heteroscedasticity checks for regression models.SCIENCE IN CHINA SERIES A-MATHEMATICS PHYSICS ASTRONOMY,44(10),1236-1252.
MLA Zhu, LX,et al."Heteroscedasticity checks for regression models".SCIENCE IN CHINA SERIES A-MATHEMATICS PHYSICS ASTRONOMY 44.10(2001):1236-1252.
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