Topics and extensions related to semiparametric mixed models with elliptical errors: estimation methods, hypothesis testing and diagnostic methods

Abstract

The aim of this work is to extend some topics investigated in the Doctor Thesis by German Pulgar related with additive semiparametric mixed models with elliptical errors. Especifically we intend to investigate nonlinear semiparametric mixed models with elliptical errors based on penalized likelihood functions. From such functions we will obtain the correspondig score functions and the Fisher information matrix. Iterative processes will be developed to obtain the maximum likelihood estimates. Also hypotesis testing and diagnostic methods such as residual analysis and sensitivity studies will be performed. Extensions for more general error correlation structures, such as autoregressive of first order, will be investigated. Finally, applications to real data and the development of computational programs in MATLAB and R will be performed.