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CONTOUR PROJECTED DIMENSION REDUCTION
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DOI：10.1214/08-AOS679.png)
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摘要
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In regression analysis, we employ contour projection (CP) to develop a new dimension reduction theory. Accordingly, we introduce the notions of the central contour subspace and generalized contour subspace. We show that both of their structural dimensions are no larger than that of the central subspace Cook [Regression Graphics (1998b) Wiley]. Furthermore, we employ CP-sliced inverse regression, CP-sliced average variance estimation and CP-directional regression to estimate the generalized contour,subspace, and we subsequently obtain their theoretical properties. Monte Carlo studies demonstrate that the three CP-based dimension reduction methods outperform their corresponding non-CP approaches when the predictors have heavy-tailed elliptical distributions. An empirical example is also presented to illustrate the usefulness of the CP method.
Keyword:
Central subspace
central contour subspace
contour projection
directional regression
generalized contour subspace
kernel contour subspace
root n-consistency
sliced average variance estimation
sliced inverse regression
sufficient contour subspace
期刊
IF:
3.7
论文数:
2.8K
被引数:
2.9W
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