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Conditional scores and optimal scores for generalized linear measurement-error models. (English) Zbl 0632.62052
A generalized linear measurement-error model is defined by a density of Y depending linearly on a covariate p-vector u which cannot be observed. Only k independent measurements $$X_ 1,...,X_ k$$ of u are available which are assumed to be normally distributed. Following M. Kendall and A. Stuart, The advanced theory of statistics. Vol. 2: Inference and relationships (1979; Zbl 0416.62001), the model is called functional if the $$u_ i$$ for a sample $$(Y_ i,X_ i)$$ are unknown constants and it is called structural if the $$u_ i$$ are i.i.d. random vectors from some unknown distribution.
In this paper for the functional case unbiased score functions are obtained by conditioning on certain sufficient statistics. The results are generalizations of earlier ones of the same authors [Ann. Stat. 13, 1335-1351 (1985; Zbl 0582.62061)] for the special case of logistic regression. For the structural case efficient score functions are derived.
Reviewer: D.Rasch

##### MSC:
 62H12 Estimation in multivariate analysis 62J99 Linear inference, regression 62J12 Generalized linear models (logistic models)