Title: Modified profile likelihood in complex models with many nuisance parameters
Authors: Claudia Di Caterina - University of Padova (Italy) [presenting]
Nicola Sartori - University of Padova (Italy)
Abstract: It is well known that usual frequentist inference procedures for a parameter of interest are generally highly inaccurate when dealing with statistical models where the number of nuisance parameters is large relative to the sample size. Among the alternative proposals put forward in the literature, the modified profile likelihood has proved to represent a valid solution to the problem. Specifically, the approximation to such pseudo-likelihood previously introduced allows us to overcome some difficulties related with its computation outside the class of exponential and group family models. Nevertheless, even this modification of the profile likelihood can be hard to obtain analytically under moderately complex scenarios. In order to further enlarge the domain of applicability of this technique, Monte Carlo simulation can be used to evaluate some expected values involved in the modified profile likelihood. It is shown how such an approach succeeds in providing a reliable inference on the parameter of interest in various frameworks, all considering a panel data structure: microeconometric fixed effects models with continuous or discrete response, models for datasets with missing values in the dependent variable or in the covariates, and parametric survival models for censored data.