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Local polynomial kernel regression for generalized linear models and quasi-likelihood functions. (English) Zbl 0818.62036
Summary: We investigate the extension of the nonparametric regression technique of local polynomial fitting with a kernel weight to generalized linear models and quasi-likelihood contexts. In the ordinary regression case, local polynomial fitting has been seen to have several appealing features in terms of intuitive and mathematical simplicity. One noteworthy feature is the better performance near the boundaries compared to the traditional kernel regression estimators. These properties are shown to carry over to generalized linear model and quasi-likelihood settings. We also derive the asymptotic distributions of the proposed class of estimators that allow for straightforward interpretation and extensions of state-of-the- art bandwidth selection methods.

MSC:
62G07 Density estimation
62J12 Generalized linear models (logistic models)
62E20 Asymptotic distribution theory in statistics
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