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Sufficient dimension reduction via inverse regression: A minimum discrepancy approach. (English) Zbl 1117.62312
Summary: A family of dimension-reduction methods, the inverse regression (IR) family, is developed by minimizing a quadratic objective function. An optimal member of this family, the inverse regression estimator (IRE), is proposed, along with inference methods and a computational algorithm. The IRE has at least three desirable properties: (1) Its estimated basis of the central dimension reduction subspace is asymptotically efficient, (2) its test statistic for dimension has an asymptotic chi-squared distribution, and (3) it provides a chi-squared test of the conditional independence hypothesis that the response is independent of a selected subset of predictors given the remaining predictors. Current methods like sliced inverse regression belong to a suboptimal class of the IR family. Comparisons of these methods are reported through simulation studies. The approach developed here also allows a relatively straightforward derivation of the asymptotic null distribution of the test statistic for dimension used in sliced average variance estimation.

62-99Statistics (MSC2000)
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