Estimation of a Conditional Mean in a Linear Regression Model

Dinesh S. Bhoj; Mohammad Ahsanullah

doi:10.1002/bimj.4710350705

Estimation of a Conditional Mean in a Linear Regression Model

Dinesh S. Bhoj, Mohammad Ahsanullah

Rutgers Camden, Mathematics

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

6 Scopus citations

Abstract

Consider the two linear regression models of Y_ij on X_ij, namely Y_ij = β_io + β_il X_ij + ε_ij,j = 1,2,…,n_i, i = 1,2, where ε_ij are assumed to be normally distributed with zero mean and common unknown variance σ². The estimated value of a mean of Y₁ for a given value of X₁ is made to depend on a preliminary test of significance of the hypothesis β₁₁ = β₂₁. The bias and the mean square error of the estimator for the conditional mean of Y₁ are given. The relative efficiency of the estimator to the usual estimator is computed and is used to determine a proper choice of the significance level of the preliminary test.

Original language	English (US)
Pages (from-to)	791-799
Number of pages	9
Journal	Biometrical Journal
Volume	35
Issue number	7
DOIs	https://doi.org/10.1002/bimj.4710350705
State	Published - 1993

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

Keywords

Bias
Conditional mean
Mean square error
Preliminary test
Regression coefficients and relative efficiency

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10.1002/bimj.4710350705

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abstract = "Consider the two linear regression models of Yij on Xij, namely Yij = βio + βil Xij + εij,j = 1,2,…,ni, i = 1,2, where εij are assumed to be normally distributed with zero mean and common unknown variance σ2. The estimated value of a mean of Y1 for a given value of X1 is made to depend on a preliminary test of significance of the hypothesis β11 = β21. The bias and the mean square error of the estimator for the conditional mean of Y1 are given. The relative efficiency of the estimator to the usual estimator is computed and is used to determine a proper choice of the significance level of the preliminary test.",

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T1 - Estimation of a Conditional Mean in a Linear Regression Model

AU - Bhoj, Dinesh S.

AU - Ahsanullah, Mohammad

PY - 1993

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N2 - Consider the two linear regression models of Yij on Xij, namely Yij = βio + βil Xij + εij,j = 1,2,…,ni, i = 1,2, where εij are assumed to be normally distributed with zero mean and common unknown variance σ2. The estimated value of a mean of Y1 for a given value of X1 is made to depend on a preliminary test of significance of the hypothesis β11 = β21. The bias and the mean square error of the estimator for the conditional mean of Y1 are given. The relative efficiency of the estimator to the usual estimator is computed and is used to determine a proper choice of the significance level of the preliminary test.

AB - Consider the two linear regression models of Yij on Xij, namely Yij = βio + βil Xij + εij,j = 1,2,…,ni, i = 1,2, where εij are assumed to be normally distributed with zero mean and common unknown variance σ2. The estimated value of a mean of Y1 for a given value of X1 is made to depend on a preliminary test of significance of the hypothesis β11 = β21. The bias and the mean square error of the estimator for the conditional mean of Y1 are given. The relative efficiency of the estimator to the usual estimator is computed and is used to determine a proper choice of the significance level of the preliminary test.

KW - Bias

KW - Conditional mean

KW - Mean square error

KW - Preliminary test

KW - Regression coefficients and relative efficiency

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Estimation of a Conditional Mean in a Linear Regression Model

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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