论文标题
使用密度差异的序数响应模型中的稳健有效估计
Robust and Efficient Estimation in Ordinal Response Models using the Density Power Divergence
论文作者
论文摘要
在现实生活中，我们经常遇到数据集，这些数据集涉及一些独立的解释变量产生一组序响应。这些顺序响应可能对应于潜在的连续潜在变量，该变量与协变量线性相关，并根据该潜在变量是否在一对（未知）剪切指定的某些合适间隔中获得值。估计未知参数（即回归系数和截止）的最有效方法是最大似然（ML）的方法。但是，数据集中的污染是以序数响应的错误指定形式，或者协变量的无限性，可能会在很大程度上使基于ML的方法可能导致完全不可靠的推断的可能性稳定。在本文中，我们基于流行的密度差异（DPD）探讨了最小距离估计程序，以产生序数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估计器（MDPDE）如何用作基于ML的经典程序的实用稳健替代方案。我们严格地开发了该估计值的几种理论特性，并提供了广泛的模拟来证实所开发的理论。
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.
