Statistical Inference of Categorical and Count Data and Its Application

本研究的目的是研究分类和计数数据模型的估计量的统计性质，并建立稳健的估计量。分类数据和计数数据不是连续的，而是离散的。泊松回归模型是分析因变量行为的标准模型，它是一个整数。然而，我们必须强加一些重要的假设。其中一个重要的假设是自变量在统计上独立于模型中的误差项。然而，当我们将定性选择机制纳入模型时，这一假设就不成立了。这些参数的估计值并不一致。问题的主要来源是模型的自变量与误差项之间的相关性。我们可以应用极大似然估计方法来得到模型的相容估计。这项研究显示了模型的几个估计量的统计性质。结果表明，极大似然估计是稳健的，而基于矩的估计器则不是。此外，在本研究中，将该模型扩展为具有有序类别自变量。

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.