Determining the dimension of the central subspace and central mean subspace
中心子空间与中心均值子空间维数的确定
The central subspace and central mean subspace are two important targets of sufficient dimension reduction. We propose a weighted chi-squared test to determine their dimensions based on matrices whose column spaces are exactly equal to the central subspace or the central mean subspace. The asymptotic distribution of the test statistic is obtained. Simulation examples are used to demonstrate the performance of this test.