Investigating effects of bandwidth selection in local polynomial regression model with applications

Article type: Research Article

Authors: Chen, Li-Pang

Affiliations: Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON, Canada | E-mail: L358CHEN@uwaterloo.ca

Correspondence: [*] Corresponding author: Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON, Canada. E-mail: L358CHEN@uwaterloo.ca.

Abstract: Cross-validation (CV) and direct plug-in (DPI) are two commonly used bandwidth selection methods in nonparametric estimation. In this paper, we compare the performance of CV and DPI methods in local polynomial kernel regression through simulation study. We consider continuous response and binary response cases, with local constant, local linear and local quadratic kernel estimators, respectively. Furthermore, we investigate the first derivatives of local quadratic kernel estimators. Our results show that CV and DPI methods excel in different cases, in terms of minimizing the Mean Integrated Squared Errors (MISE); the results are also verified in empirical studies.

Keywords: Cross-validation, directly plug-in method, first-order derivative, generalized linear model, local polynomial estimator

DOI: 10.3233/MAS-180457

Journal: Model Assisted Statistics and Applications, vol. 14, no. 1, pp. 31-45, 2019