Covariance projective resampling informative predictor subspace for multivariate regression

In this paper, we newly define a covariance projective resampling informative predictor subspace (covPRIPS) besides an existing projective resampling informative predictor subspace (Ko and Yoo in J Korean Stat Soc 51:1117–1131, 2022; PRIPS). To clarify the relation between covPRIPS and the central subspace, two mild conditions are assumed to hold. Under the conditions, covPRIPS becomes the smallest subspace to contain the central subspace up to date while being nested in PRIPS. Two possible benefits of covPRIPS over PRIPS are no necessity of slicing tTY and intuitive interpretation of the role of tTY. Numerical studies show that the estimation method of covPRIPS is competitive with the inverse mean method of PRIPS.