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Abstract:
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Traditional variable selection methods are model-based and may suffer from possible model misspecification. Sufficient dimension reduction provides us a way to find sufficient dimensions without a parametric model. Each reduced variable is a linear combination of all the original variables. In this talk, focusing on the sufficient dimensions in the regression mean function, we combine the ideas of sufficient dimension reduction and variable selection to propose a shrinkage estimation method, sparse MAVE. The sparse MAVE can exhaustively estimate dimensions in mean function, while selecting informative covariates simultaneously without assuming any particular model or particular distribution on the predictor variables. Furthermore, we propose a modified BIC criterion to effectively estimate the dimension of the mean function.
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