Optimal zone for bandwidth selection in semiparametric models

• Main Authors: LI, Jialiang, ZHANG, Wenyang, WU, Zhengxiao
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2011
• Subjects: optimal bandwidth; cross-validation; asymptotic mean square error; Taylor series expansion; Neumann series approximation; Statistical Theory; Statistics and Probability
• Online Access: https://ink.library.smu.edu.sg/soe_research_all/11
• Institution: Singapore Management University

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.