Sufficient Dimension Folding in Regression via Distance Covariance for Matrix‐valued Predictors

Authors

Wenhui Sheng, Marquette UniversityFollow
Qingcong Yuan, Miami University - Oxford

Document Type

Article

Publication Date

2-2020

Publisher

Wiley

Source Publication

Statistical Analysis and Data Mining

Source ISSN

1932-1864

Abstract

In modern data, when predictors are matrix/array‐valued, building a reasonable model is much more difficult due to the complicate structure. However, dimension folding that reduces the predictor dimensions while keeps its structure is critical in helping to build a useful model. In this paper, we develop a new sufficient dimension folding method using distance covariance for regression in such a case. The method works efficiently without strict assumptions on the predictors. It is model‐free and nonparametric, but neither smoothing techniques nor selection of tuning parameters is needed. Moreover, it works for both univariate and multivariate response cases. In addition, we propose a new method of local search to estimate the structural dimensions. Simulations and real data analysis support the efficiency and effectiveness of the proposed method.

Comments

Accepted version. Statistical Analysis and Data Mining, Vol. 13, No. 1 (February 2020): 71-82. DOI. © 2020 Wiley. Used with permission.

Recommended Citation

Sheng, Wenhui and Yuan, Qingcong, "Sufficient Dimension Folding in Regression via Distance Covariance for Matrix‐valued Predictors" (2020). Mathematical and Statistical Science Faculty Research and Publications. 42.
https://epublications.marquette.edu/math_fac/42