Determinant Efficiencies in Ill-Conditioned Models
نویسندگان
چکیده
منابع مشابه
Determinant Efficiencies in Ill-Conditioned Models
The canonical correlations between subsets of OLS estimators are identified with design linkage parameters between their regressors. Known collinearity indices are extended to encompass angles between each regressor vector and remaining vectors. One such angle quantifies the collinearity of regressors with the intercept, of concern in the corruption of all estimates due to ill-conditioning. Mat...
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Ridge versions of an ill-conditioned system are alleged to ‘‘act more like an orthogonal system’’ than the system itself. Alternatives, called surrogates and based on the conditioning of linear systems, are shown to yield smaller expected mean squares than OLS, and uniformly smaller residual sums of squares than ridge. Ridge and surrogate solutions are compared on several marques of orthogonali...
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A ridge version of an ill–conditioned system is long held to “act more like an orthogonal system” than the system itself. Surrogate models exist also having smaller expected mean square than OLS, and surrogate solutions are seen to have uniformly smaller residual sums of squares than ridge. Ridge and surrogate solutions are compared on several hallmarks of orthogonality, to include conditioning...
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A square system of linear equations is ‘ill-conditioned’ when the norm of the corresponding inverse matrix is large. This norm bounds the size of the solution, and measures how close the system is to being inconsistent: it is thus of fundamental computational significance. We generalize this idea from linear equations to inclusions governed by closed convex processes, and hence to ‘conic linear...
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ژورنال
عنوان ژورنال: Journal of Probability and Statistics
سال: 2011
ISSN: 1687-952X,1687-9538
DOI: 10.1155/2011/182049