On Limited Dependent Variable Models: Maximum Likelihood Estimation and Test of One-sided Hypothesis
研究了误差项具有对数凹密度函数的受限因变量模型，证明了极大似然估计的存在性和渐近正态性，并给出了单侧假设检验中似然比统计量的渐近分布。
The limited dependent variable models with errors having log-concave density functions are studied here. For such models with normal errors, the asymptotic normality of the maximum likelihood estimator was established by Amemiya [1]. We show, when the density of the error distribution is log-concave, that the maximum likelihood estimator exists with arbitrarily large probability for large sample sizes, and is asymptotically normal. The general theory presented here includes the important special cases of normal, logistic, and extreme value error distributions. The main results are established under rather weak conditions. It is also shown that, under the null hypothesis, the asymptotic distribution of the likelihood ratio statistic for testing a one-sided alternative hypothesis is a weighted sum of chi-squares.