Dimension reduction in regression without matrix inversion
نویسندگان
چکیده
منابع مشابه
Dimension Reduction Regression in R
Regression is the study of the dependence of a response variable on a collection predictors collected in . In dimension reduction regression, we seek to find a few linear combinations , such that all the information about the regression is contained in these linear combinations. If is very small, perhaps one or two, then the regression problem can be summarized using simple graphics; for exampl...
متن کاملKernel Dimension Reduction in Regression∗
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 ass...
متن کاملSliced Regression for Dimension Reduction
By slicing the region of the response (Li, 1991, SIR) and applying local kernel regression (Xia et al., 2002, MAVE) to each slice, a new dimension reduction method is proposed. Compared with the traditional inverse regression methods, e.g. sliced inverse regression (Li, 1991), the new method is free of the linearity condition (Li, 1991) and enjoys much improved estimation accuracy. Compared wit...
متن کاملDimension-Reduction in Binary Response Regression
The idea of dimension-reduction without loss of information can be quite helpful for guiding the construction of summary plots in regression without requiring a pre-specified model. Focusing on the central subspace, we investigate such “sufficient” dimension-reduction in regressions with a binary response. Three existing methods, SIR and pHd and SAVE, and one new method DOC are studied for thei...
متن کاملComment: Fisher Lecture: Dimension Reduction in Regression
This paper puts dimension reduction into the historical context of sufficiency, efficiency and principal component analysis, and opens up an avenue toward efficient dimension reduction via maximum likelihood estimation of inverse regression. I congratulate Professor Cook for this insightful and groundbreaking work. My discussion will focus on two points that explore and extend Cook’s ideas. The...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Biometrika
سال: 2007
ISSN: 0006-3444,1464-3510
DOI: 10.1093/biomet/asm038