![Sample our Bioscience journals, sign in here to start your access, Latest two full volumes FREE to you for 14 days]({"type":"image" , "src" : "/sda/5925/TOC-Subject-Sample-2021-Bioscience.jpg"})
Abstract
It is important to detect the variance heterogeneity in regression model because efficient inference requires that heteroscedasticity is taken into consideration if it really exists. For the varying-coefficient partially linear regression models, however, the problem of detecting heteroscedasticity has received very little attention. In this paper, we present two classes of tests of heteroscedasticity for varying-coefficient partially linear regression models. The first test statistic is constructed based on the residuals, in which the error term is from a normal distribution. The second one is motivated by the idea that testing heteroscedasticity is equivalent to testing pseudo-residuals for a constant mean. Asymptotic normality is established with different rates corresponding to the null hypothesis of homoscedasticity and the alternative. Some Monte Carlo simulations are conducted to investigate the finite sample performance of the proposed tests. The test methodologies are illustrated with a real data set example.
MSC (2010):
Acknowledgements
The authors are grateful to the Editor and two anonymous referees for their constructive comments which have greatly improved this paper.
Disclosure statement
No potential conflict of interest was reported by the authors.
Funding
The research work is supported by the National Natural Science Foundation of China under Grant No. [11171065], [11301073], [11401094], the Natural Science Foundation of Jiangsu Province of China under Grant No. [BK20140617], [BK20141326] the Research Fund for the Doctoral Program of Higher Education of China under Grant No. [20120092110021] and the Social Science Fund of the Ministry of Education No. [13YJC910006].