Abstract
A multivariate errors-in-variables model in the matrix form can be written as X=U+E, Y=UA′+WB+F, where X (n×p) and Y (n×q) are observed matrices, E and F are error matrices whose rows are normally distributed, W (n×k) is a known matrix of rank k, and U, A and B are unknown matrices. We consider the problems of testing linear hypotheses: (i) H 0: AR=K and (ii) H 0: S′A=L, where R, K, S and L are known matrices, and we derive the likelihood ratio tests for testing these hypotheses.
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References
Bansal, N. K. (1987). Some statistical inferences on latent variables. Ph.D. Dissertation, University of Pittsburgh, Pennsylvania.
Basu, A. P. (1969). On some tests for several linear relations, J. Roy. Statist. Soc. Ser. B. 31, 65–71.
Gleser, L. J. and Watson, G. S. (1973). Estimation of a linear transformation, Biometrika, 60, 525–534.
Rao, C. R. (1973). Linear Statistical Inference and Its Application, 2nd ed., Wiley, New York.
Villegas, C. (1964). Confidence region for a linear relation, Ann. Math. Statist., 35, 780–788.
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Bansal, N.K. Testing linear hypotheses in errors in variables model. Ann Inst Stat Math 42, 581–596 (1990). https://doi.org/10.1007/BF00049309
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DOI: https://doi.org/10.1007/BF00049309