KERNEL DIMENSION REDUCTION IN REGRESSION
KERNEL DIMENSION REDUCTION IN REGRESSION
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DOI：
10.1214/08-aos637
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发表时间：
2009-08-01
影响因子：
4.5
通讯作者：
Jordan, Michael I.
中科院分区：
文献类型：
--
作者：
Fukumizu, Kenji;Bach, Francis R.;Jordan, Michael I.
提出了一种新的充分降维方法。我们的方法直接来自SDR的公式，根据协变量X与响应Y的条件独立性，给定X在中心子空间上的投影[cf. J. Amer统计学家。Assoc.86（1991）316-342和Regression Graphics（1998）Wiley]。我们表明，这种条件独立断言可以在再生核希尔伯特空间的条件协方差算子的特点，我们展示了如何这种特性导致中央子空间的M-估计。由此产生的估计是一致的弱条件下，特别是，我们不需要强加的线性或椭圆度的条件，通常调用SDR方法的种类。我们还提出了实证结果表明，新的方法在实践中是有竞争力的。
We present a new methodology for sufficient dimension reduction (SDR). Our methodology derives directly from the formulation of SDR in terms of the conditional independence of the covariate X from the response Y, given the projection of X on the central subspace [cf. J. Amer Statist. Assoc. 86 (1991) 316-342 and Regression Graphics (1998) Wiley]. We show that this conditional independence assertion can be characterized in terms of conditional covariance operators on reproducing kernel Hilbert spaces and we show how this characterization leads to an M-estimator for the central subspace. The resulting estimator is shown to be consistent under weak conditions; in particular, we do not have to impose linearity or ellipticity conditions of the kinds that are generally invoked for SDR methods. We also present empirical results showing that the new methodology is competitive in practice.