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Abstract:
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In some applications involving multivariate linear regression, it is of scientific interest to identify/select responses that have at least one nonzero regression coef- ficient. We refer to these 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 we call it a static response. Therefore, we can classify the responses into three categories: the dynamic responses, the ancillary responses, and the static responses. We derive an algorithm to identify these response variables, and provide an estimator of the regression coefficients based on the selection result. The scientific insights and efficiency gains obtained by the proposed procedure are illustrated with data.
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