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Estimation of a Two-Limit Tobit model with generalized Box-Cox transformation and unknown censoring thresholds

机译：估计具有广义箱COX转换的双限制TOBBIT模型和未知的审查阈值

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This article considers estimation of a Two-Limit Tobit model with generalized Box-Cox transformation and unknown censoring thresholds. The maximum likelihood estimates of the censoring thresholds are the smallest and largest elements of the order statistic of the transformed dependent variable for the uncensored subsample. Conditional on the estimated censoring thresholds and the parameter of the generalized Box-Cox transformation, the model is a standard Tobit model. If the dependent variable is scaled by the geometric mean of its absolute values for the uncensored subsample, then currently available software for estimation of Tobit models may be used in conjunction with a grid search over the Box-Cox parameter to determine the globalmaximum likelihood estimates. The advantage of the models proposed in this article is that: 1) use of estimated censoring thresholds serve to directly eliminate the understatement of tail probabilities that can result from use of fixed thresholds, and 2) use of the generalized Box-Cox transformation allows greater flexibility in the shape of the distribution used to model quantitative variation in the uncensored subsample, as well as greater flexibility in the tail probabilities of the censored subsample.
机译：本文考虑了具有广义盒式Cox转换和未知的审查阈值的双限制Tobit模型的估计。审查阈值的最大似然估计是未经审查的子样本的转换相关变量的顺序统计的最小和最大元素。条件在估计的审查阈值和广义盒式Cox转换的参数上，该模型是标准的Tobit模型。如果从属变量通过其绝对值的绝对值的绝对值的几何平均值来缩放，则目前可用的用于估计Tobit模型的软件可以与盒子Cox参数的网格搜索结合使用以确定全球性达到似然估计。本文提出的模型的优点在于：1）使用估计的抗思阈值用于直接消除可以通过使用固定阈值而导致的尾部概率的轻描处，并且2）推广盒-COX变换的使用允许更大用于模拟未经审查的子样本中的定​​量变化的分布形状的灵活性，以及​​缩短的附带的尾部概率中的更大灵活性。

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