Utilizing initial estimates in estimating the coefficients in a linear model

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

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)219-222
Number of pages4
JournalJournal of the American Statistical Association
Volume69
Issue number345
DOIs
StatePublished - 1974
Externally publishedYes

Fingerprint

Linear Model
Least Squares Estimator
Coefficient
Estimator
Estimate
Inaccurate
Replication
Coefficients
Class
Least squares estimator

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Utilizing initial estimates in estimating the coefficients in a linear model. / Mayer, Lawrence S.; Singh, Jagbir; Willke, Thomas A.

In: Journal of the American Statistical Association, Vol. 69, No. 345, 1974, p. 219-222.

Research output: Contribution to journalArticle

Mayer, Lawrence S. ; Singh, Jagbir ; Willke, Thomas A. / Utilizing initial estimates in estimating the coefficients in a linear model. In: Journal of the American Statistical Association. 1974 ; Vol. 69, No. 345. pp. 219-222.
@article{b0c4df63ad3b4d6488ad31cbd45ffa83,
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.}",
year = "1974",
doi = "10.1080/01621459.1974.10480157",
language = "English (US)",
volume = "69",
pages = "219--222",
journal = "Journal of the American Statistical Association",
issn = "0162-1459",
publisher = "Taylor and Francis Ltd.",
number = "345",

}

TY - JOUR

T1 - Utilizing initial estimates in estimating the coefficients in a linear model

AU - Mayer, Lawrence S.

AU - Singh, Jagbir

AU - Willke, Thomas A.

PY - 1974

Y1 - 1974

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.

UR - http://www.scopus.com/inward/record.url?scp=84950661072&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84950661072&partnerID=8YFLogxK

U2 - 10.1080/01621459.1974.10480157

DO - 10.1080/01621459.1974.10480157

M3 - Article

AN - SCOPUS:84950661072

VL - 69

SP - 219

EP - 222

JO - Journal of the American Statistical Association

JF - Journal of the American Statistical Association

SN - 0162-1459

IS - 345

ER -