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Biometrika 1991 78(2):442-445; doi:10.1093/biomet/78.2.442
© 1991 by Biometrika Trust
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MISCELLANEA

On the unreplicated ultrastructural model

CHI-LUN CHENG1 and JOHN W. VAN NESS2

1Department of Mathematics, Tamkang University Tamsui, Taiwan
2Program in Mathematical Sciences, University of Texas at Dallas Richardson, Texas 75083–0688, U.S.A.

Dolby's (1976) ultrastructural model is investigated with emphasis on the case with no replications and one of the error variances known. It is shown that, in this situation, the maximum likelihood estimators are not consistent. The method of moments estimators are consistent and asymptotically normal and best in Fisher's sense within a broad class of asymptotically normal estimators discussed by Gleser (1983). Some connections with the errors-in-variables model are examined.

Key Words: Asymptotic normality; Consistency • Errors-in-variables • Functional relation • Maximum likelihood • Structural relation • Ultrastructural relation


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