1992 Fiscal Year Final Research Report Summary
Statistical Theory of Qualitative Variable Model and its Applications to Micro Economic Data
| Project/Area Number |
03630018
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
Economic statistics
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| Research Institution | Aoyama Gakuin University (1992)
Rissho University (1991) |
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Principal Investigator |
YOSHIZOE Yasuto Aoyama Gakuin University, Department of Economics, Professor, 経済学部, 教授 (80062868)
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| Project Period (FY) |
1991 – 1992
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| Keywords | binary regression / coding error / influence function / robust estimation / M-推定量 |
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| Research Abstract |
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.
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