In real life, we frequently come across data sets that involve some independent explanatory variable(s) generating a set of ordinal responses. These ordinal responses may correspond to an underlying continuous latent variable, which is linearly related to the covariate(s), and takes a particular (ordinal) label depending on whether this latent variable takes value in some suitable interval specified by a pair of (unknown) cut-offs. The most efficient way of estimating the unknown parameters (i.e., the regression coefficients and the cut-offs) is the method of maximum likelihood (ML). However, contamination in the data set either in the form of misspecification of ordinal responses, or the unboundedness of the covariate(s), might destabilize the likelihood function to a great extent where the ML based methodology might lead to completely unreliable inferences. In this paper, we explore a minimum distance estimation procedure based on the popular density power divergence (DPD) to yield robust parameter estimates for the ordinal response model. This paper highlights how the resulting estimator, namely the minimum DPD estimator (MDPDE), can be used as a practical robust alternative to the classical procedures based on the ML. We rigorously develop several theoretical properties of this estimator, and provide extensive simulations to substantiate the theory developed.

翻译：在现实生活中，我们经常遇到涉及某些独立解释变量生成一组有序响应的数据集。这些有序响应可能对应于一个潜在的连续潜变量，该变量与协变量呈线性关系，并根据该潜变量是否位于由一对（未知）截断点指定的某个适当区间内，而取特定的（有序）标签。估计未知参数（即回归系数和截断点）最有效的方法是最大似然（ML）法。然而，数据集中以有序响应误设或协变量无界形式存在的污染，可能会在很大程度上破坏似然函数的稳定性，导致基于ML的方法可能得出完全不可靠的推断。在本文中，我们探索了一种基于流行密度功率散度（DPD）的最小距离估计程序，以产生有序响应模型的稳健参数估计。本文强调了所得估计量，即最小DPD估计量（MDPDE），如何作为基于ML的经典方法的实用稳健替代方案。我们严格推导了该估计量的若干理论性质，并进行了大量模拟以证实所建立的理论。