Abstract: A multivariate subset (or `partially') reduced-rank regression model is considered as an extension of the usual multivariate reduced-rank model. In the model, the reduced-rank coefficient structure is specified to occur for a subset of the response variables only, which allows for more general situations and can lead to more efficient modeling than the usual reduced-rank model. The maximum likelihood estimation of parameters, likelihood ratio testing for rank, and large sample properties of estimators for this partially reduced-rank model are developed. An empirical procedure to aid in identification of the possible subset reduced-rank structure is suggested. Two numerical examples are examined to illustrate the methodology for the proposed model.
Key words and phrases: Canonical correlations, covariance adjustment, likelihood ratio test, maximum likelihood estimator, partitioned coefficient matrix, partially reduced-rank regression.