On a Criterion for Simultaneous Extrapolation in Nonfull Rank Normal Regression

In recent work by O'Reilly, a necessary and sufficient condition for the existence of an unbiased estimate of the distribution function of a "future" observation was given. The result was obtained under the condition that the model had full rank. Here, the result is generalized to any...

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Bibliographic Details
Published in:The Annals of statistics 1976-05, Vol.4 (3), p.625-628
Main Author: O'Reilly, Federico J.
Format: Article
Language:English
Subjects:
62F10
62J05
Distribution functions
estimability of a distribution
Mathematical extrapolation
Mathematical vectors
MVUE (minimum variance unbiased estimate)
Short Communications
Sufficient conditions
Unbiased estimators
validity of extrapolation
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Summary:In recent work by O'Reilly, a necessary and sufficient condition for the existence of an unbiased estimate of the distribution function of a "future" observation was given. The result was obtained under the condition that the model had full rank. Here, the result is generalized to any number of future observations and the full rank condition is relaxed. The corresponding uniformly minimum variance unbiased estimator is identified from the density estimates given by Ghurye and Olkin.
ISSN:0090-5364
2168-8966
DOI:10.1214/aos/1176343469