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ЖУРНАЛЫ // Theory of Stochastic Processes // Архив

Theory Stoch. Process., 2007, том 13(29), выпуск 4, страницы 69–81 (Mi thsp236)

Эта публикация цитируется в 1 статье

Comparing the efficiency of estimates in concrete errors-in-variables models under unknown nuisance parameters

Alexander Kukusha, Andrii Malenkob, Hans Schneeweissc

a Department of Mathematical Analysis, Kyiv National Taras Shevchenko University, Kyiv, Ukraine
b Department of Probability Theory and Mathematical Statistics, Kyiv National Taras Shevchenko University, Kyiv, Ukraine
c University of Muenchen, Germany

Аннотация: We consider a regression of y on x given by a pair of mean and variance functions with a parameter vector $\theta$ to be estimated that also appears in the distribution of the regressor variable $x.$ The estimation of $\theta$ 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 $\alpha$ of $\theta,$ 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 efficient than the $CS$ estimator. We focus on the loglinear Poisson, the Gamma, and the logit model.

Ключевые слова: Mean-variance model, measurement error model, quasi score estimator, corrected score estimator, nuisance parameter, optimality property.

MSC: 62J05, 62J12, 62F12, 62F10, 62H12, 62J10

Язык публикации: английский



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