Journal of the American Statistical Association vol:92 issue:440 pages:1536-1545
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.