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Abstract:
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Estimating an inverse regression space typically requires a tuning parameter such as a number of slices in slicing method or bandwidth in kernel estimation approach, which then increases difficulties for multivariate responses. In this paper, we use Fourier transform idea to avoid such difficulties while the proposed method easily incorporates with multivariate responses. We further develop Fourier transform method to deal with sparse issue, categorical predictor variables and large p, small n data. Asymptotic tests as well as the sparse eigen-decomposition method for dimensionality tests are obtained. Simulation studies and a real data show the efficacy of our proposed methods.
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