POSITIVE-SHRINKAGE AND PRETEST ESTIMATION IN MULTIPLE REGRESSION: A MONTE CARLO STUDY WITH APPLICATIONS

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ENAYETUR RAHEEM S.M.; EJAZ AHMED S.

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Journal: JOURNAL OF THE IRANIAN STATISTICAL SOCIETY (JIRSS) Year:2011 | Volume:10 | Issue:2 Page(s): 267-289

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Information Journal Paper

Title

POSITIVE-SHRINKAGE AND PRETEST ESTIMATION IN MULTIPLE REGRESSION: A MONTE CARLO STUDY WITH APPLICATIONS

Author(s)

ENAYETUR RAHEEM S.M. | EJAZ AHMED S. | Issue Writer Certificate

Keywords

DATA ANALYSISQ4

JAMES-STEIN ESTIMATIONQ4

LASSOQ4

MONTE CARLO SIMULATIONQ4

MULTIPLE REGRESSIONQ4

PRETEST ESTIMATIONQ4

QUADRATIC RISKQ4

RMSEQ4

SHRINKAGE ESTIMATIONQ4

Abstract

Consider a problem of predicting a response variable using a set of covariates in a linear regression model. If it is a priori known or suspected that a subset of the covariates do not significantly contribute to the overall fit of the model, a restricted model that excludes these covariates, may be sufficient. If, on the other hand, the subset provides useful information, shrinkage method combines restricted and unrestricted estimators to obtain the parameter estimates. Such an estimator outperforms the classical maximum likelihood estimators. Any prior information may be validated through preliminary test (or pretest), and depending on the validity, may be incorporated in the model as a parametric restriction. Thus, pretest estimator chooses between the restricted and unrestricted estimators depending on the outcome of the preliminary test. Examples using three real life data sets are provided to illustrate the application of shrinkage and PRETEST ESTIMATION. Performance of positive-shrinkage and pretest estimators are compared with unrestricted estimator under varying degree of uncertainty of the prior information. Monte Carlo study reconfirms the asymptotic properties of the estimators available in the literature.

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APA: Copy

ENAYETUR RAHEEM, S.M., & EJAZ AHMED, S.. (2011). POSITIVE-SHRINKAGE AND PRETEST ESTIMATION IN MULTIPLE REGRESSION: A MONTE CARLO STUDY WITH APPLICATIONS. JOURNAL OF THE IRANIAN STATISTICAL SOCIETY (JIRSS), 10(2), 267-289. SID. https://sid.ir/paper/117827/en

Vancouver: Copy

ENAYETUR RAHEEM S.M., EJAZ AHMED S.. POSITIVE-SHRINKAGE AND PRETEST ESTIMATION IN MULTIPLE REGRESSION: A MONTE CARLO STUDY WITH APPLICATIONS. JOURNAL OF THE IRANIAN STATISTICAL SOCIETY (JIRSS)[Internet]. 2011;10(2):267-289. Available from: https://sid.ir/paper/117827/en

IEEE: Copy

S.M. ENAYETUR RAHEEM, and S. EJAZ AHMED, “POSITIVE-SHRINKAGE AND PRETEST ESTIMATION IN MULTIPLE REGRESSION: A MONTE CARLO STUDY WITH APPLICATIONS,” JOURNAL OF THE IRANIAN STATISTICAL SOCIETY (JIRSS), vol. 10, no. 2, pp. 267–289, 2011, [Online]. Available: https://sid.ir/paper/117827/en

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