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- W2096871125 abstract "Several anomalies in the foundations of ridge regression from the perspective of constrained least-square (LS) problems were pointed out in Jensen & Ramirez. Some of these so-called anomalies, attributed to the non-monotonic behaviour of the norm of unconstrained ridge estimators and the consequent lack of sufficiency of Lagrange's principle, are shown to be incorrect. It is noted in this paper that, for a fixed Y, norms of unconstrained ridge estimators corresponding to the given basis are indeed strictly monotone. Furthermore, the conditions for sufficiency of Lagrange's principle are valid for a suitable range of the constraint parameter. The discrepancy arose in the context of one data set due to confusion between estimates of the parameter vector, β, corresponding to different parametrization (choice of bases) and/or constraint norms. In order to avoid such confusion, it is suggested that the parameter β corresponding to each basis be labelled appropriately. Plusieurs anomalies ont été récemment relevées par Jensen et Ramirez (2008) dans les fondements théoriques de la “ridge regression” considérée dans une perspective de moindres carrés constraints. Certaines de ces anomalies ont été attribuées au comportement non monotone de la norme des “ridge-estimateurs” non contraints, ainsi qu'au caractère non suffisant du principe de Lagrange. Nous indiquons dans cet article que, pour une valeur fixée de Y, la norme des ridge-estimateurs correspondant à une base donnée sont strictement monotones. En outre, les conditions assurant le caractère suffisant du principe de Lagrange sont satisfaites pour un ensemble adéquat de valeurs du paramètre contraint. L'origine des anomalies relevées se trouve donc ailleurs. Cette apparente contradiction prend son origine, dans le contexte de l'étude d'un ensemble de données particulier, dans la confusion entre les estimateurs du vecteur de paramètres β correspondant à différentes paramétrisations (associées à différents choix d'une base) et/ou à différentes normes. Afin d'éviter ce type de confusion, il est suggéré d'indexer le paramètre de façon adéquate au moyen de la base choisie." @default.
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- W2096871125 date "2010-06-18" @default.
- W2096871125 modified "2023-09-25" @default.
- W2096871125 title "Anomalies in the Foundations of Ridge Regression: Some Clarifications" @default.
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- W2096871125 doi "https://doi.org/10.1111/j.1751-5823.2010.00113.x" @default.
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