Local Polynomial Estimation in Multiparameter Likelihood Models
将局部多项式拟合的非参数回归技术扩展到多参数似然模型，证明了边界行为等优良性质，并推导了渐近一致性和正态性，可用于聚类二元数据的剂量反应建模。
Abstract The nonparametric regression technique of local polynomial fitting is extended to multiparameter likelihood models. Some well-known appealing features of local polynomial smoothers, such as the behavior at the boundary, are shown to carry over to the multiparameter case. Asymptotic consistency and normality of the resulting estimators are derived under suitable regularity conditions. This work is motivated by the need for a nonparametric alternative to parametric dose-response models for clustered binary data. Probability models for clustered binary response data include a success probability parameter and one or more correlation parameters. The proposed local polynomial estimators can play an important role as a diagnostic tool or to suggest the form of the functional relationships in parametric likelihood models. As an illustration, it is shown how the local likelihood estimation procedure can be implemented for fitting a dose-response curve based on the beta-binomial model. A data example and a small simulation study demonstrate the method's applicability.