Efficient Semiparametric Estimation of Censored and Truncated Regressions via a Smoothed Self-Consistency Equation
提出一种基于似然的半参数估计方法，通过平滑自洽方程估计残差密度，用于删失回归（Tobit）模型，得到渐近有效的参数估计，并简要给出截断回归的类似结果。
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 smooth enough to be used in a practical implementation of the profile likelihood estimator, but is sufficiently close to the nonparametric maximum likelihood estimator to allow estimation of the semiparametric efficient score. The parameter estimates obtained by solving the estimated score equations are then asymptotically efficient. A summary of analogous results for truncated regression is also given. Copyright The Econometric Society 2004.