Reduced-rank mean estimation for projective-resampling informative predictor subspace

Abstract

Recently, a projective-resampling informative predictor subspace for a multivariate regression of Y is an element of Rr|X is an element of Rp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textbf{Y}\in \mathbb {R}<^>r|\textbf{X}\in \mathbb {R}<^>p$$\end{document} with r >= 2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r\ge 2$$\end{document} and its estimation methods have been defined and developed. The methods necessitate significant numbers of resampling, which are not theoretically derived. To reduce the number of resamplings and concurrently enhance estimation accuracy, it is considered to substitute random resampling with response dimension reduction. Theoretically, it is demonstrated that this substitution, at least, does not result in the loss of information on E(Y|X)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E(\textbf{Y}|\textbf{X})$$\end{document}. Numerical studies validate its potential superiority over existing methods.