A1286
Title: Response variable selection in multivariate linear regression
Authors: Zhihua Su - University of Florida (United States) [presenting]
Kshitij Khare - University of Florida (United States)
Abstract: Response variable selection and subsequent estimation of the regression coefficients in multivariate linear regression are discussed. Because of the asymmetric roles of the predictors and responses in regression, response variable selection is markedly different from the usual predictor variable selection. When a response is inferred to have coefficients zero, it should not be simply removed from subsequent estimation. Instead, its relationship is analyzed with the responses that have nonzero coefficients, called dynamic responses. If it is correlated with the dynamic responses given all other responses, it should be retained to improve the estimation efficiency of the nonzero coefficients as an ancillary statistic. Otherwise, it can be removed from further inference (leading to significant resource savings in high-dimensional settings), called a static response. Therefore, the responses can be classified into three categories: dynamic, ancillary, and static. An algorithm is derived to identify these response variables and provide an estimator of the regression coefficients based on the selection result.
