双尾 Tobit 模型中 LAD 估计的渐近正态性

摘要

Due to accuracies of measurement tools or mechanisms ,response variables are limited by the range of the measurement ,whose exact values larger or less than measurement limits can not be observed . There are many studies on parameter estimation and inferences in Tobit regression models with response values less than some fixed values . However ,work with response constrained by both maximum and minimum values is rare .Here ,the least absolute deviation (LAD) estimates of regression parameters were proposed and their statistical properties were studied . Finally , numerical simulation studies were conducted to show that the proposed method performs well .%由于测量仪器或者测量方法精确度的影响，响应变量受到测量范围的限制，当大于最大测量值或者小于最小测量值时，其确切值不能观测到。当响应变量只受最小值或最大值限制时，有关回归模型（Tobit 模型）中参数估计及其统计推断性质的研究已比较多。这里在响应变量同时受到最大值和最小值限制的情形下，讨论了回归模型（双尾 Tobit 模型）中参数 LAD 估计的构造，且在一定的条件下，证明了该 LAD 估计的弱相合性和渐近正态性。最后，利用数值模拟研究结果评估了所提方法的效果。