Journal ArticleDOI
Ridge Analysis Following a Preliminary Test of the Shrunken Hypothesis
TLDR
In this article, the normal distribution theory likelihood ratio statistic for the corresponding composite hypothesis is derived, and a small sample F-test is shown to be conservative, and the asymptotic distribution of the likelihood ratio provides a large sample test of the RISE optimality of any restricted Ridge family of solutions.Abstract:
RIDGE ANALYSIS is of interest when some generalized Ridge regression coefficient vectors are significantly more likely to have Mean Squared Error (MSE) optimality properties than is any uniformly SHRUNKEN version of the ordinary least squares estimator. The normal distribution theory likelihood ratio statistic for the corresponding composite hypothesis is derived, and a small sample F-test is shown to be conservative. The asymptotic distribution of the likelihood ratio provides a large sample test of the RISE optimality of any restricted Ridge FAMILY of solutions. The likelihood approach for solution selection WITHIN a given family is then compared and contrasted with some snggestions of Mallows [8] and Allen [1] and with a new, non-stochastic criterion, SSCBC.read more
Citations
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Journal ArticleDOI
Generalized Cross-Validation as a Method for Choosing a Good Ridge Parameter
TL;DR: The generalized cross-validation (GCV) method as discussed by the authors is a generalized version of Allen's PRESS, which can be used in subset selection and singular value truncation, and even to choose from among mixtures of these methods.
Journal ArticleDOI
A Simulation Study of Some Ridge Estimators
TL;DR: In this article, the authors identify 10 promising algorithms for ridge regression and systematically evaluate and compare them using Monte Carlo methods, and three algorithms perform well overall, including a two-parameter estimator.
Journal ArticleDOI
Ridge Regression and James-Stein Estimation: Review and Comments
TL;DR: The literature of ridge regression and James-Stein estimation is broadly reviewed in this paper, and critical comments are interpolated on a number of papers, expressing their viewpoints on ridge regression, and their antipathy to its mechanical use.
Journal ArticleDOI
Mean squared error matrix comparisons between biased estimators — An overview of recent results
Götz Trenkler,Helge Toutenburg +1 more
TL;DR: In this article, a systematic report on mean squared error matrix comparisons of competing biased estimators is given, where the parameter vector to be estimated is assumed to belong to a subset of the p-dimensional Euclidean space.
Journal ArticleDOI
Performance of some new preliminary test ridge regression estimators and their properties
TL;DR: In this paper, the problem of estimation of the regression coefficients in a multiple regression model is considered under multicollinearity situation when it is suspected that regression coefficients may be restricted to a subspace.
References
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Journal ArticleDOI
Ridge regression: biased estimation for nonorthogonal problems
TL;DR: In this paper, an estimation procedure based on adding small positive quantities to the diagonal of X′X was proposed, which is a method for showing in two dimensions the effects of nonorthogonality.
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Some Comments on Cp
TL;DR: In this article, the typical configuration of a Cp plot when the number of variables in the regression problem is large and there are many weak effects is studied, and a particular configuration that is very commonly seen can arise in a simple way.
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Ridge Regression: Applications to Nonorthogonal Problems
TL;DR: In this paper, the use of ridge regression methods is discussed and recommendations are made for obtaining a better regression equation than that given by ordinary least squares estimation. But the authors focus on the RIDGE TRACE which is a two-dimensional graphical procedure for portraying the complex relationships in multifactor data.
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Generalized Inverses, Ridge Regression, Biased Linear Estimation, and Nonlinear Estimation
TL;DR: In this article, the authors discuss a class of biased linear estimators employing generalized inverses and establish a unifying perspective on nonlinear estimation from nonorthogonal data.