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.

在二进制回归模型中，响应概率函数f是固定但任意的，我们表明MLE在大多数情况下（例如概率和逻辑）并不强大。因此，我们构建了一类强大的M估算物，当存在以F形式的规范误差时，这些M-估计性也很健壮。我们详细讨论了逻辑模型，因为它比其他模型具有一些优势。我们发现一类M-估算物，它们以F的功能形式对规范错误，假设F任意F作为真实模型，并研究其属性。2。然后，我们介绍了描述二进制回归模型中合理错误的编码误差模型。我们的M估计也对这种错误也很强。3。最后，我们给出了对F中的规格错误在定性上具有鲁棒性的M估计，同时在真实模型上是一致且渐近效率的。进一步的主题是，当存在观察错误和规范错误时，没有估计可以是一致的（在论文中明确定义了概念）。因此，我们必须依靠一些自适应方法来估计响应概率而不假设F的刚性形式作为估计二进制回归模型的最终解决方案。作者提出了朝向这一方向的贝叶斯方法。