Likelihood corrections for the incidental parameter problem in Poisson distributed panel data

Abstract

In statistical analysis of data we are interested in understanding or estimating certain aspects of the probability distribution generating the data. The aspects we are interested in does not always relate to all the parameters of the probability distribution. In this case the parameters that are not of primary interest is termed \enquote{nuisance parameters} and need to be dealt with in order to gain insight on the parameters of interest. We will in this thesis focus on a special case of this problem where the nuisance parameters are especially problematic. The problem we are interested in is when the number of nuisance parameters increases with the data, such that increasing the number of observations does not improve estimates of the nuisance parameters. Briefly explained the incidental parameter problem occurs when parameters that are not of interest increase in number with the data at a rate large enough to disturb the maximum likelihood estimates of the parameters that are of interest, in the sense that the maximum likelihood estimators for the parameters of interest will no longer be consistent. There are several proposed solutions to the incidental parameter problem. In this thesis we will compare an approximate conditional likelihood and four modifications to the profile likelihood when applied to a model of Poisson distributed panel data with two fixed effect. We will study their behaviour on simulated data, and in a simulation study compare the accuracy of estimators based on these likelihood functions.