A1025
Title: Response variable selection in multivariate linear regression
Authors: Kshitij Khare - University of Florida (United States) [presenting]
Abstract: In some applications involving multivariate linear regression, it is of scientific interest to identify/select responses that have at least one nonzero regression coefficient. These are referred to as dynamic responses. Because of the asymmetric roles of the predictors and responses in regression, response variable selection is markedly different from the usual predictor variable selection. In particular, when a response is inferred to have all regression coefficients equal to zero, it should not be simply removed from subsequent estimation. If it is correlated with the dynamic responses given all other responses, it should be retained to improve estimation efficiency as an ancillary statistic. Otherwise, it can be removed from further inference, and it is called a static response. Therefore, the responses can be classified into three categories: dynamic responses, ancillary responses, and static responses. An algorithm is derived to identify these response variables, and an estimator of the regression coefficients is provided based on the selection result. The scientific insights and efficiency gains obtained by the proposed procedure are illustrated with data. Consistency of the selection procedures and asymptotic properties of the estimators are established both for the large sample size and the high-dimensional small sample size settings.
