Multivariate seeded dimension reduction

A recently introduced seeded dimension reduction approach enables existing sufficient dimension reduction methods to be used in regressions with n < p. The dimension reductionisaccomplished through successive projectionsof seed matrices ona subspace to contain the central subspace. In the article, we will develop a seeded dimension reduction for multivariate regression, whose responses are multi-dimensional. For this we suggest two conditions that the dimension reduction is attained without the loss of information of the central subspace. Based on this, we construct possible candidate seed matrices. Numerical studies and two data analyses are presented.