L2E ESTIMATOR FOR THE CATEGORICAL MODEL WITH ELASTIC NET PENALTY
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The logistic regression model is an important generalized linear model for the categorical data. The maximum likelihood estimation is mostly used in estimating the parameters of the logistic regression model. However, the maximum likelihood estimation is very sensitive to outliers which will cause the inaccuracies of the fitted parameters and model selection in high-dimensional regression. Chi and Scott (2014) demonstrated by simulation that minimizing the integrated square error or L2 estimation (L2E) is a robust method to fit 2-class categorical models. They also showed that the L2E estimation method can select the right model even in the presence of many outliers in high dimensional scenarios. In my thesis, I extended the L2E estimation method from 2-class to 3-class based on the MM algorithm by Chi and Scott (2014). Then I demonstrated the properties above for 2-class categorical models are also applicable to 3-class ones.