Optimal zone for bandwidth selection in semiparametric models

Abstract

We study the general problem of bandwidth selection in semiparametric regression. By expanding the higher-order terms in the Taylor series for the asymptotic mean-squared error, we provide a theoretical justification for the earlier empirical observations of an optimal zone of bandwidths in the literature. Based on the idea of cross-validating parametrical estimates, we further introduce a novel bandwidth selector for semiparametric models. The method is demonstrated by numerical studies to be able to preserve the selected bandwidth within the optimal zone. This data-driven cross-validation method may also be applicable for model diagnosis and longitudinal data settings. Examples from two clinical trials are provided to illustrate the applications.

Keywords:

• optimal bandwidth
• cross-validation
• asymptotic mean square error
• Taylor series expansion
• Neumann series approximation

Acknowledgements

We thank the Associate Editor and two referees for their expert comments that have greatly improved this paper. This project was partially supported by grants from Academic Research Funding R-155-000-082-112 and National Medical Research Council NMRC/NIG/0054/2009.