22

Annals of the Institute of Statistical Mathematics

Springer

1993

45

3

531-540

Orthogonality , profile likelihood , measurement error model , conditional model , likelihood ratio statistic - marginal posterior distribution , marginal posterior distribution

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In this paper, we consider the estimation of the slope parameter of a simple structural linear regression model when the reliability ratio (Fuller (1987),Measurement Error Models, Wiley, New York) is considered to be known. By making use of an orthogonal transformation of the unknown parameters, the maximum likelihood estimator of and its asymptotic distribution are derived. Likelihood ratio statistics based on the profile and on the conditional profile likelihoods are proposed. An exact marginal posterior distribution of , which is shown to be at-distribution is obtained. Results of a small Monte Carlo study are also reported.

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