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An asymptotically efficient likelihood-based semiparametric estimator is derived for the censored regression (tobit) model, based on a new approach for estimating the density function of the residuals in a partially observed regression. Smoothing the self-consistency equation for the nonparametric maximum likelihood estimator of the distribution of the residuals yields an integral equation, which in some cases can be solved explicitly. The resulting estimated density is…

二元选择与删失回归模型中分布自由估计量的效率界AI 解读

We derive lower bounds on the asymptotic variances for regular distribution-free estimators of the parameters of the binary choice model and the censored regression (Tobit) model. A distribution-free (or semiparametric) estimator is one that does not require any assumption about the distribution of the stochastic error term in the model, apart from regularity conditions. For the binary choice model, we obtain an explicit lower bound for the asymptotic variance for the slope…

二元选择模型的分布无关极大似然估计量AI 解读

is a given function of the exogenous variables z and unknown parameters 9, representing the systematic component of the utility difference, and F is the distribution function of the random component of the utility difference. This paper describes a method of estimating the parameters 9 without assuming any functional form for the distribution function F, and proves that this estimator is consistent. F is also consistently estimated. The method uses maximum likelihood…