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Biometrika 1978 65(3):535-540; doi:10.1093/biomet/65.3.535
© 1978 by Biometrika Trust
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The unreplicated ultrastructural relation: Large sample properties

W. M. PATEFIELD

Department of Mathematics, University of Salford

Dolby (1976) introduced a model which is a synthesis of the linear structural and functional relations. The consistency of the slope estimator he proposed depends on the sequence of incidental parameters. When these parameters have finite variance the estimator is inconsistent. It is shown that a simple adjustment produces a consistent estimator of familiar form. Dolby incorrectly proposes that the asymptotic covariances of the estimators may be obtained from Fisher's information matrix. The correct asymptotic covariances are given and estimators suggested. Corresponding results are presented for the analogous linear functional relation with correlated errors.

Key Words: Asymptotic covariance • Consistency • Functional relation • Maximum likelihood • Structural relation • Ultrastructural relation


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