Utilizing initial estimates in estimating the coefficients in a linear model

Lawrence S. Mayer; Jagbir Singh; Thomas A. Willke

doi:10.1080/01621459.1974.10480157

Utilizing initial estimates in estimating the coefficients in a linear model

Lawrence S. Mayer
, Jagbir Singh
, Thomas A. Willke

Arizona State University

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

A procedure which utilizes an initial estimate to estimate the coefficients in a linear mode is introduced. A linear model containing replications with the same input matrix is considered and a class of two-stage estimators is defined. Optimal estimators in the class are determined, and it is shown that the proposed estimators are better than the corresponding single-sample least squares estimator if the initial estimate is accurate, and are as good (asymptotically) as the corresponding single-sample least squares estimator if the initial estimate is inaccurate.

Original language	English (US)
Pages (from-to)	219-222
Number of pages	4
Journal	Journal of the American Statistical Association
Volume	69
Issue number	345
DOIs	https://doi.org/10.1080/01621459.1974.10480157
State	Published - Mar 1974

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1080/01621459.1974.10480157

Cite this

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title = "Utilizing initial estimates in estimating the coefficients in a linear model",

abstract = "A procedure which utilizes an initial estimate to estimate the coefficients in a linear mode is introduced. A linear model containing replications with the same input matrix is considered and a class of two-stage estimators is defined. Optimal estimators in the class are determined, and it is shown that the proposed estimators are better than the corresponding single-sample least squares estimator if the initial estimate is accurate, and are as good (asymptotically) as the corresponding single-sample least squares estimator if the initial estimate is inaccurate.",

author = "Mayer, \{Lawrence S.\} and Jagbir Singh and Willke, \{Thomas A.\}",

note = "Funding Information: * Lawrence S. Mayer is mistant professor. Department of Statistics, Virginia Polytechnic Institute and State University. Blacksburg, Va. 24061. Jagbir Singh is sasbtant professor, Division of Statistics, and Thomas A. Wake is vice-provost, both at Ohio State University, Columbus. Ohio 43210. The authors wish to thank the referees for their excellent commenta. and the first author acknowledges the partial support of the National Institute of Mental Health, Grant Nos. 1 R03 MH 21454-01 and 1 R03 MH 23177-01.",

year = "1974",

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doi = "10.1080/01621459.1974.10480157",

language = "English (US)",

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AU - Singh, Jagbir

AU - Willke, Thomas A.

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N2 - A procedure which utilizes an initial estimate to estimate the coefficients in a linear mode is introduced. A linear model containing replications with the same input matrix is considered and a class of two-stage estimators is defined. Optimal estimators in the class are determined, and it is shown that the proposed estimators are better than the corresponding single-sample least squares estimator if the initial estimate is accurate, and are as good (asymptotically) as the corresponding single-sample least squares estimator if the initial estimate is inaccurate.

AB - A procedure which utilizes an initial estimate to estimate the coefficients in a linear mode is introduced. A linear model containing replications with the same input matrix is considered and a class of two-stage estimators is defined. Optimal estimators in the class are determined, and it is shown that the proposed estimators are better than the corresponding single-sample least squares estimator if the initial estimate is accurate, and are as good (asymptotically) as the corresponding single-sample least squares estimator if the initial estimate is inaccurate.

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Utilizing initial estimates in estimating the coefficients in a linear model

Abstract

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