Sufficient dimension folding in regression via distance covariance for matrix‐valued predictors. (26th October 2019)

• Record Type: Journal Article
• Authors: Sheng, Wenhui; Yuan, Qingcong
• Is Part Of: Statistical analysis and data mining. Volume 13:Number 1(2020)
• Page Start: 71
• Page End: 82
• Publication Date: 2019-10-26
• Subjects: central dimension folding subspace -- distance covariance -- sufficient dimension folding; Data mining -- Statistical methods -- Periodicals; 006.312
• DOI: 10.1002/sam.11442
• Languages: English
• ISSNs: 1932-1864

Abstract

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.