Comparing the efficiency of estimates in concrete errors-in-variables models under unknown nuisance parameters
We consider a regression of y on x given by a pair of mean and variance functions with a parameter vector θ to be estimated that also appears in the distribution of the regressor variable x. The estimation of θ is based on an extended quasi score (QS) function. Of special interest is the case where...
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| Date: | 2007 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2007
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| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/4514 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Comparing the efficiency of estimates in concrete errors-in-variables models under unknown nuisance parameters / A. Kukush, A. Malenko, H. Schneeweiss // Theory of Stochastic Processes. — 2007. — Т. 13 (29), № 4. — С. 69–81. — Бібліогр.: 11 назв.— англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | We consider a regression of y on x given by a pair of mean and variance functions with a parameter vector θ to be estimated that also appears in the distribution of the regressor variable x. The estimation of θ is based on an extended quasi score (QS) function. Of special interest is the case where the distribution of x depends only on a subvector α of θ, which may be considered a nuisance parameter. A major application of this model is the classical measurement error model, where the corrected score (CS) estimator is an alternative to the QS estimator. Under unknown nuisance parameters
we derive conditions under which the QS estimator is strictly more аfficient than the CS estimator. We focus on the loglinear Poisson, the Gamma, and the logit model. |
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