Efficiency Bounds for Distribution-Free Estimators of the Binary Choice and the Censored Regression Models
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 ↓
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AI 根据所提供的论文材料归类：摘要直接研究二元选择模型的半参数效率界，同时讨论固定删失点的回归模型，最直接对应给定目录中的离散选择。
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二元选择与删失回归模型中分布自由估计量的效率界
- 研究问题
- 在仅对误差分布施加正则条件时，二元选择与固定删失点回归的参数估计能达到怎样的渐近方差下界，未知分布造成多少信息损失？
- 方法与思路
- 作者推导正则半参数估计量的渐近方差下界，比较参数与半参数模型，并分别讨论误差中位数为零、分布对称及自适应估计的条件。
- 材料陈述的贡献
- 摘要称，仅以零中位数限制识别时，二元选择截距无正则半参数估计量；对称性可使其下界有限，删失回归的界可涵盖截距，自适应估计通常不可行。
- 阅读关注点
- 读全文应区分截距的识别与正则可估性，核对对称性怎样改变效率界，并检查参数界与半参数界相等及自适应估计可行的条件。
- 阅读边界
- 摘要的分布自由仍要求正则条件，部分截距结论依赖零中位数或对称性；下界结果不能直接说明某个可行估计量达到效率界或有限样本表现。
原文摘要
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 parameters, or more generally the parameters of a nonlinear regression function in the underlying latent variable model, but we find that there is no regular semiparametric estimator of the constant term (identified by requiring the error distribution to have zero median). Lower bounds are also obtained under the further assumption that the error distribution is symmetric, and in this case there is a finite lower bound for the constant term too. Comparison of the bounds with those for the classical parametric problem shows the loss of information due to lack of a priori knowledge of the functional form of the error distribution. We give the conditions for equality of the parametric and semiparametric lower bounds (in which case adaptive estimation may be possible), both with and without the assumption of a symmetric error distribution. In general, adaptive estimation is not possible, but one special case where these conditions hold is when the regression function is linear and the explanatory variables have a multivariate normal distribution. The Tobit model considered here is the censored nonlinear regression model, with a fixed censoring point. We again give an explicit lower bound for the asymptotic variance for the regression parameters, this time including a constant term (if the error term has zero median). Comparison with the corresponding lower bound for the parametric case shows that adaptive estimation is in general not possible for this model.