Comparative analysis of different cross-validation bandwidth selectors in kernel regression estimators

The performance of kernel regression estimation mainly depends on the selection of bandwidth. The cross-validation is a simple and effective selection method by using leave-one-out strategy. In this paper, we compare three different cross-validation bandwidth selectors based on Arithmetic Mean (CVAM), Geometric Mean (CVGM) and Harmonic Mean (CVHM) within three common kernel regression estimators, i.e., Nadaraya-Watson kernel estimator (NWKE), Priestley-Chao kernel estimator (PCKE) and Gasser-Müller kernel estimator (GMKE). Firstly, we analyse the mathematical properties of arithmetic mean, geometric mean and harmonic mean. Then, we conduct the an experiments to compare the bandwidth selection of above-mentioned cross-validation methods in terms of regression accuracy and stability. Finally, the derived conclusions give some guidelines for the selections of kernel regression estimators and the corresponding cross-validation bandwidth selectors in the practical applications.