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We proposed a new method to estimate the intra-cluster adjusted central subspace for regressions with multivariate responses. Following Setodji and Cook (2004), we made use of the k-means algorithm to cluster the observed response vectors. Our method was designed to recover the intracluster information and outperformed previous method with respect to estimation accuracies on both the central subspace and its dimension. It also allowed us to test the predictor effects in a model-free approach. Simulation and a real data example were given to illustrate our methodology. AMS 2000 subject classifications: Primary 62G08, 62H12; secondary 62H30.

A minimum discrepancy approach to multivariate dimension reduction via $k$-means inverse regression