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Biometrika 1973 60(1):65-72; doi:10.1093/biomet/60.1.65
© 1973 by Biometrika Trust
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Linear regression with randomly dispersed parameters

BARR ROSENBERG

University of California Berkeley

Consider a collection of individual linear regression models, in which each individual parameter vector is independently drawn from a common multivariate normal distribution and is fixed over successive observations on that individual. Maximum likelihood estimators of the mean and dispersion of the parameters and of the disturbance variance are derived. These estimators yield empirical Bayes estimators of the individual parameter veotors. The properties of the estimators are exhibited in the case where the parameter dispersion is known.

Key Words: Regression • Stochastic parameters • Variance components • Maximum likelihood • Empirical Bayes


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