### 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.

Original language | English (US) |
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Pages (from-to) | 899-917 |

Number of pages | 19 |

Journal | Statistica Sinica |

Volume | 16 |

Issue number | 3 |

State | Published - Jul 1 2006 |

### Keywords

- Canonical correlations
- Covariance adjustment
- Likelihood ratio test
- Maximum likelihood estimator
- Partially reduced-rank regression
- Partitioned coefficient matrix

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty

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## Cite this

*Statistica Sinica*,

*16*(3), 899-917.