Variance reduction in multiparameter likelihood models

Local likelihood modeling is a unified and effective approach to establishing the dependence of a response variable, which can be of various types, on independent variables. Therefore, these models have become popular in a wide range of applications. There is an increasing interest in employing multiparameter local likelihood models to investigate trends of sample extremes in environmental statistics. When sample maxima are modeled by a generalized extreme value distribution, the sample size is small in general and local likelihood estimation exhibits a large variation. In this article variance reduction techniques are employed to improve the efficiency of the inference. A simulation study and an application to annual maximum temperatures show that our methods are very effective in finite samples.