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Abstract:
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We propose a new sufficient dimension folding method for regression in which the predictors are matrix- or array- valued. The method is model-free and avoids strong assumptions on the distribution of X. It also does not require kernel or smoothing techniques, neither does it require choosing tuning parameters, such as the number of slices. Moreover, it can deal with both scalar response and multivariate response scenarios. A bootstrap method is introduced to estimate the structural dimension. Asymptotic properties of the estimator is studied. Simulations and real data analysis support the efficiency and effectiveness of the method.
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