A simple and effective bandwidth selector for local polynomial quasi-likelihood regression

초록

Local quasi-likelihood methods are powerful nonparametric techniques that can be applied to a variety of regression problems where the conventional least squares approach is not appropriate. They are particularly useful for analyzing regression data with binary and count responses. In this paper, we propose a new bandwidth selector for local quasi-likelihood regression estimation. It eschews conventional cross-validation that requires fitting the data repeatedly with one or some of the data leaved out. Our proposal needs only a single fit of the whole regression function, and does not call for selection of secondary tuning parameters as in plug-in rules. The method is based on a uniform stochastic expansion for the estimated quasi-likelihood, which we derive in this paper. We investigate the finite sample properties of the proposed bandwidth selector through a Monte Carlo simulation.

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