Sankhya: The Indian Journal of Statistics

1994, Volume 56, Series B, Pt. 1, pp. 95--106

PREDICTIVE INFERENCE FOR THE MULTILINEAR MODEL WITH ERRORS HAVING MULTIVARIATE $t$-DISTRIBUTION AND FIRST ORDER AUTO-CORRELATION STRUCTURE

By

SHAHJAHAN KHAN and M. SAFIUL HAQ, *The University of Western Ontario*

SUMMARY. Prediction distribution for the future responses from the multilinear model with the multivariate student-t error distribution and first order auto-correlation structure has been derived. First the marginal likelihood equation of the auto-correlation coefficient, r has been obtained which yielded the maximum likelihood estimate of r . Then the structural relation of the model has been utilized for the derivation of the prediction distribution of the future responses. Construction of a (1-a ) 100% prediction region and some special cases are discussed.

*AMS (1980) subject classification.* Primary 62J05; secondary 62A25.

*Key words and phrases.* Linear model, multilinear model, prediction distribution, prediction region, multivariate $t$-distribution, first order auto-correlation, marginal likelihood equation.