Local Polynomial Kernel Regression for Generalized Linear Models and Quasi-Likelihood Functions
研究了将局部多项式核回归扩展到广义线性模型和拟似然函数，证明其在边界处表现优于传统核回归，并推导了估计量的渐近分布以支持带宽选择。
Abstract 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. Key Words: BandwidthBoundary effectsLocal likelihoodLogistic regressionNonparametric regressionPoisson regression