Principal Fitted Components for Dimension Reduction in Regression
نویسندگان
چکیده
منابع مشابه
Principal Fitted Components for Dimension Reduction in Regression
We provide a remedy for two concerns that have dogged the use of principal components in regression: (i) principal components are computed from the predictors alone and do not make apparent use of the response, and (ii) principal components are not invariant or equivariant under full rank linear transformation of the predictors. The development begins with principal fitted components [Cook, R. ...
متن کاملOptimal dimension reduction and transform coding with mixture principal components
This paper addresses the problem of resource allocation in local linear models for non-linear principal component analysis (PCA). In the local PCA model, the data space is partitioned into regions and PCA is performed in each region. Our primary result is that the advantage of these models over conventional PCA has been signiicantly underestimated in previous work. We apply local PCA models to ...
متن کاملNonparametric Principal Components Regression
In ordinary least squares regression, dimensionality is a sensitive issue. As the number of independent variables approaches the sample size, the least squares algorithm could easily fail, i.e., estimates are not unique or very unstable, (Draper and Smith, 1981). There are several problems usually encountered in modeling high dimensional data, including the difficulty of visualizing the data, s...
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 via principal variables
For many large-scale datasets it is necessary to reduce dimensionality to the point where further exploration and analysis can take place. Principal variables are a subset of the original variables and preserve, to some extent, the structure and information carried by the original variables. Dimension reduction using principal variables is considered and a novel algorithm for determining such p...
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: Statistical Science
سال: 2008
ISSN: 0883-4237
DOI: 10.1214/08-sts275