CONTOUR PROJECTED DIMENSION REDUCTION

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 subsp...

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Bibliographic Details
Published in:The Annals of statistics 2009-12, Vol.37 (6B), p.3743-3778
Main Authors: Luo, Ronghua, Wang, Hansheng, Tsai, Chih-Ling
Format: Article
Language:English
Subjects:
62G08
62G20
62G35
Applications
central contour subspace
Central subspace
contour projection
Degrees of freedom
Dimensionality reduction
directional regression
Distribution theory
Eigenvalues
Estimate reliability
Estimating techniques
Estimation methods
Estimators
Exact sciences and technology
General topics
generalized contour subspace
Insurance, economics, finance
kernel contour subspace
Linear inference, regression
Linear regression
Mathematics
Probability and statistics
Regression analysis
Sciences and techniques of general use
sliced average variance estimation
sliced inverse regression
sqrt{n}-consistency
Statistical variance
Statistics
Stock markets
Studies
sufficient contour subspace
Surface contours
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Summary: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 out-perform 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.
ISSN:0090-5364
2168-8966
DOI:10.1214/08-AOS679