Statistical Inference of Categorical and Count Data and Its Application

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The purpose of this research was to investigate the statistical properties of the estimators of the categorical and count data model and to establish the robust estimator. The categorical and count data is not continuous but discrete. The Poisson regression model is the standard model for analysis of the behavior of the dependent variable which is an integer. However, we have to impose some important assumptions. One of the significant assumptions is that the independent variables are statistically independent from the error term in the model. However, such assumption is not hold when we incorporate the qualitative choice mechanism into the model. The estimators of the parameters are not consistent. The main source of the problem is the correlation between the independent variable and the error term of the model. We can apply the maximum likelihood estimation method to get the consistent estimator of the model. This research shows the statistical properties of several estimators for the model. The results show that the maximum likelihood estimation is robust and the moment based estimator is not. Further, the model is extended to have the ordered categorical independent variable in this research.