TY - JOUR

T1 - Heteroscedasticity testing for regression models

T2 - A dimension reduction-based model adaptive approach

AU - Zhu, Xuehu

AU - Chen, Fei

AU - Guo, Xu

AU - ZHU, Lixing

N1 - Funding Information:
Lixing Zhu was supported by a grant from the University Grants Council of Hong Kong , Hong Kong, China. Fei Chen was supported by a grant from the National Natural Science Foundation of China (Grant No. 11261064 ). Xu Guo was supported by the Natural Science Foundation of Jiangsu Province, China , Grant No. BK20150732 . This work was also supported in part by the Natural Science Foundation of China Grant No. 11401465 . The authors thank the editor, the associate editor and two anonymous referees for their constructive comments and suggestions which led to a substantial improvement of an early manuscript.

PY - 2016/11/1

Y1 - 2016/11/1

N2 - Heteroscedasticity testing is of importance in regression analysis. Existing local smoothing tests suffer severely from curse of dimensionality even when the number of covariates is moderate because of use of nonparametric estimation. A dimension reduction-based model adaptive test is proposed which behaves like a local smoothing test as if the number of covariates was equal to the number of their linear combinations in the mean regression function, in particular, equal to 1 when the mean function contains a single index. The test statistic is asymptotically normal under the null hypothesis such that critical values are easily determined. The finite sample performances of the test are examined by simulations and a real data analysis.

AB - Heteroscedasticity testing is of importance in regression analysis. Existing local smoothing tests suffer severely from curse of dimensionality even when the number of covariates is moderate because of use of nonparametric estimation. A dimension reduction-based model adaptive test is proposed which behaves like a local smoothing test as if the number of covariates was equal to the number of their linear combinations in the mean regression function, in particular, equal to 1 when the mean function contains a single index. The test statistic is asymptotically normal under the null hypothesis such that critical values are easily determined. The finite sample performances of the test are examined by simulations and a real data analysis.

KW - Heteroscedasticity testing

KW - Model-adaption

KW - Sufficient dimension reduction

UR - http://www.scopus.com/inward/record.url?scp=84974667207&partnerID=8YFLogxK

U2 - 10.1016/j.csda.2016.04.009

DO - 10.1016/j.csda.2016.04.009

M3 - Article

AN - SCOPUS:84974667207

VL - 103

SP - 263

EP - 283

JO - Computational Statistics and Data Analysis

JF - Computational Statistics and Data Analysis

SN - 0167-9473

ER -