SGER- Estimation of Binary Choice and Nonparametric Censored Regression Models

这项探索性研究由两个截然不同的部分组成。第一部分，也是主要部分考虑了二元选择模型的估计问题。这是一个统计模型，其中因变量(研究人员试图使用观察到的解释变量来解释或预测的变量)只能取两个值。对于这个模型，有三个应用研究人员感兴趣的价值估计。一个是预测函数的参数集，可以用来预测结果。感兴趣的其他值是选择概率和边际效应。前者为研究人员提供了观察到作为观察到的解释变量的函数的因变量的值的概率，而后者确定了解释变量的值的变化对该概率的影响。现有的估计要么不能同时估计所有感兴趣的值，要么要求对因变量和解释变量之间的关系进行非常严格的假设。相反，在这项研究项目中开发的程序并不强加严格的假设，但能够联合估计感兴趣的三个价值。这项研究的第二部分涉及删失回归模型的估计，这是一种统计模型，在该模型中，不会观察到因变量的值超过固定常数，这里称为删减点。应用工作中遇到的许多数据集都显示了该模型的特征。这项研究项目开发了一种新的程序，能够估计超出审查点的区域的预测函数。如果没有更强有力的假设，使用现有方法是无法做到这一点的。

This exploratory research is comprised of two distinct parts. The first and main part considers estimation of a binary choice model. This is a statistical model where the dependent variable (the one researchers are trying to explain or predict using observed explanatory variables) can take only two values. For this model, there are three values applied researchers are interested in estimating. One is the set of the parameters of the prediction function, which can be used to predict outcomes. The other values of interest are choice probabilities and marginal effects. The former provides researchers with the probability of observing a value of the dependent variable as a function of observed explanatory variables, and the latter determines the effect of a change in the value of the explanatory variable on this probability. Existing estimation either cannot simultaneously estimate all values of interest, or they require very strict assumptions on the relationship between the dependent and explanatory variables. In contrast, the procedures developed in this research project do not impose strict assumptions, yet enable joint estimation of the three values of interest. The second part of this research involves the estimation of a censored regression model, which is a statistical model where the dependent variable is never observed to take a value exceeding a fixed constant, referred to here as the censoring point. Many data sets encountered in applied work exhibit this model's features. This research project develops a new procedure which enables estimation of the prediction function in the region beyond the censoring point. This cannot be done using existing methods without stronger assumptions.