Statistical Theory of Qualitative Variable Model and its Applications to Micro Economic Data

定性变量模型统计理论及其在微观经济数据中的应用

基本信息

批准号：
03630018
负责人：
YOSHIZOE Yasuto
金额：
$ 0.96万
依托单位：
Aoyama Gakuin University (1992)Rissho University (1991)
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1991
资助国家：
日本
起止时间：
1991 至 1992
项目状态：
已结题

项目摘要

In the binary regression model where the response probability function F is fixed but arbitrary, we showed that mle is not robust in most cases such as probit and logic. We thus constructed a class of robust M-estimates which also turn out to be robust when there exists the specification error in the form of F. We discussed the logic model in detail since it has some advantages over other models.In a forthcoming paper entitled "Robust Estimation of the Binary Regression Model,"the following problems are discussed.1. We find a class of M-estimates which are robust against the specification errors in the functional form of F, assuming arbitrary F as the true model, and investigate their properties.2. We then introduce the coding error model which describes the plausible errors in the binary regression model. Our M-estimate is also robust against this kind of errors.3. Finally, we give the M-estimate which is qualitatively robust against specification errors in F, and at the same time, is consistent and asymptotically efficient at the true model.A further topic is that when there exist both observation errors and the specification error, then no estimate can be consistent(the concept is clearly defined in the paper). Hence we must depend on some adaptive methods of estimating response probability without assuming a rigid form of F, as the final solution to the estimation of the binary regression model. The author has proposed a Bayesian method towards this direction.

在响应概率函数 F 固定但任意的二元回归模型中，我们表明，mle 在大多数情况下（例如概率和逻辑）并不稳健。因此，我们构建了一类鲁棒的 M 估计，当存在 F 形式的规范误差时，它也被证明是鲁棒的。我们详细讨论了逻辑模型，因为它比其他模型有一些优势。在即将发表的题为《二元回归模型的鲁棒估计》讨论了以下问题： 1．我们发现一类M-估计，假设任意F 作为真实模型，对F 函数形式的规范误差具有鲁棒性，并研究它们的性质。2．然后我们介绍编码误差模型，它描述二元回归模型中的合理误差。我们的 M 估计对于此类错误也具有稳健性。3．最后，我们给出了 M 估计，该估计对 F 中的规范误差具有定性鲁棒性，同时在真实模型中是一致且渐近有效的。进一步的主题是，当同时存在观测误差和规范误差时，那么没有任何估计可以是一致的（论文中明确定义了这个概念）。因此，我们必须依靠一些估计响应概率的自适应方法，而不是假设 F 的刚性形式，作为二元回归模型估计的最终解决方案。作者朝着这个方向提出了贝叶斯方法。