A Critique of Some Ridge Regression Methods: Comment

Nostrand, R. Craig Van

doi:10.2307/2287389

Cited by 9 publications

(4 citation statements)

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“…For Pattern 2, Cell(2,2) was selected with n 22 = 75. The results for the simulation analysis of Pattern 1 are given in the last coluniversally accepted by the statistical community (Smith & Campbell, 1980), nor has it been shown to be the best strategy under all data conditions (see the review of simulation studies by Nostrand, 1980). Research on its applicability to the unbalanced ANOVA case would be useful.…”

Section: Simulation Resultsmentioning

confidence: 99%

“…O. MULLIGAN, D. WONG, AND P. THOMPSON universally accepted by the statistical community (Smith & Campbell, 1980), nor has it been shown to be the best strategy under all data conditions (see the review of simulation studies by Nostrand, 1980). Research on its applicability to the unbalanced ANOVA case would be useful.…”

Section: Discussion and Alternative Proceduresmentioning

confidence: 99%

“…Ridge regression ( PROC RIDGEREG ) is available in the SAS system (documented in the SAS/ETS guide). However, ridge regression has not been universally accepted by the statistical community (Smith & Campbell, 1980), nor has it been shown to be the best strategy under all data conditions (see the review of simulation studies by Nostrand, 1980). Research on its applicability to the unbalanced ANOVA case would be useful.…”

Section: Discussion and Alternative Proceduresmentioning

confidence: 99%

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Robustness properties of nonorthogonal analysis of variance.

Milligan¹,

Wong²,

Thompson³

1987

Psychological Bulletin

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Nonorthogonal analysis of variance (ANOV A) is defined as a factorial ANOVA with differing numbers of subjects in the cells. Despite the volume of literature in the psychological journals dealing with the problems of nonorthogonal ANOVA, little attention has been focused on the robustness properties of the corresponding hypothesis tests. Monte Carlo results are presented for the two-way ANOVA design indicating that all of the standard computational routines for the unequal cell size case are nonrobust. This occurs when the assumptions of homogeneity of variance or normality are violated. The user is cautioned against collecting such data. If such data must be analyzed, then alternative or supplemental analysis strategies should be used. Alternative approaches would include simulation, rank transformation, modified ANOVA procedures, and alternative developments in linear models, such as nonparametric factorial ANOVA.

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Section: Simulation Resultsmentioning

confidence: 99%

Section: Discussion and Alternative Proceduresmentioning

confidence: 99%

Section: Discussion and Alternative Proceduresmentioning

confidence: 99%

See 1 more Smart Citation

Robustness properties of nonorthogonal analysis of variance.

Milligan¹,

Wong²,

Thompson³

1987

Psychological Bulletin

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“…However, the abundance of methods and studies on their development indicates that each of them has its own area of suitable applications, and there is no superior method. This well-known fact is based primarily on numerous studies by simulation and analysis of the estimators under different conditions [29,9,21,38,14,20].…”

Section: Introductionmentioning

confidence: 99%

A Dual estimator as a tool for solving regression problems

Gordinsky¹

2013

Electron. J. Statist.

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This paper discusses a parameter estimation method that employs an unusual estimator called the Dual estimator. For a linear regression model, we obtain two alternative estimators by subtracting or adding a certain vector to the vector of the Ordinary Least Squares Estimator (OLSE). One of them strictly dominates the latter. Moreover, under the normality assumption this estimator is unbiased, and consistent, and has significantly smaller variance than the OLSE. The use of a priori information is a universal way to choose a better alternative. An important property of the proposed method is the possibility of using the strict inequalities as a priori information. In particular, if the external information is that the L2-norm of the OLS estimate exceeds the same norm of a vector of true coefficients, one can choose a better alternative without additional parameters. If it is known that the parameter is restricted by a linear non-strict inequality, the method has a smaller Mean Squared Error than a Constrained Least Squares technique. Finally, a priori information on two possible parameter values can be successfully used for the experimental confirmation of one of two alternative theories, which is illustrated by a verification of the General Theory of Relativity based upon astronomical data.

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Ridge Regression

Birkes

Dodge

1993

Alternative Methods of Regression

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A Critique of Some Ridge Regression Methods: Comment

Cited by 9 publications

References 0 publications

Robustness properties of nonorthogonal analysis of variance.

Robustness properties of nonorthogonal analysis of variance.

A Dual estimator as a tool for solving regression problems

Ridge Regression

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