Detection of marginal heteroscedasticity for partial linear single-index models

Abstract

We consider the detection of marginal heteroscedasticity for partial linear single-index models. We regress absolute values of residuals on each covariate by marginal univariate nonparametric smoothing with a sequence of bandwidths, then a ordinary least squares estimator between the quadratic nonparametric estimate and bandwidths are obtained. We rank least squares estimates and obtain the top ranked covariates according to a ridge-type absolute coefficient ratio. Then, a refinement step is based to the smoothly clipped absolute deviation penalization method for marginal heteroscedastic detection. Simulation studies and a real dataset are conducted to demonstrate the performance of the proposed method.

Keywords:

• Marginal heteroscedasticity
• Kernel smoothing
• Single-index
• Ridge-type absolute coefficient ratio
• SCAD

Acknowledgments

The authors thank the editor, the associate editor, and a referee for their constructive suggestions that helped us to improve the early manuscript. Bingqing Lin’s research was supported by the National Natural Science Foundation of China (NSFC) (Grant No. 11701386). This article was done when the second author visited the Department of Biostatistics, School of Public Health, University of Texas at Houston, Houston, TX, USA.