Improved best linear unbiased estimators for the simple linear regression model using double ranked set sampling schemes

In this paper, we consider the best linear unbiased estimators (BLUEs) based on double ranked set sampling (DRSS) and ordered DRSS (ODRSS) schemes for the simple linear regression model with replicated observations. We assume three symmetric distributions for the random error term, i.e., normal, Lap...

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Published in:Communications in statistics. Theory and methods Vol. 45; no. 12; pp. 3541 - 3561
Main Authors: Haq, Abdul, Brown, Jennifer, Moltchanova, Elena
Format: Journal Article
Language:English
Published: Philadelphia Taylor & Francis 17.06.2016
Taylor & Francis Ltd
Subjects:
Best linear unbiased estimator
Economic models
Estimators
Mathematical models
Normality
Order statistics
Primary: 62D05; Secondary: 62F10
Ranked set sample
Regression
Regression analysis
Relative efficiency
Sampling
Sensitivity analysis
Simple linear regression model
Statistics
Symmetry
ISSN:0361-0926, 1532-415X
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Abstract In this paper, we consider the best linear unbiased estimators (BLUEs) based on double ranked set sampling (DRSS) and ordered DRSS (ODRSS) schemes for the simple linear regression model with replicated observations. We assume three symmetric distributions for the random error term, i.e., normal, Laplace and some scale contaminated normal distributions. The proposed BLUEs under DRSS (BLUEs-DRSS) and ODRSS (BLUEs-ODRSS) are compared with the BLUEs based on ordered simple random sampling (OSRS), ranked set sampling (RSS), and ordered RSS (ORSS) schemes. These estimators are compared in terms of relative efficiency (RE), RE of determinant (RED), and RE of trace (RET). It is found that the BLUEs-ODRSS are uniformly better than the BLUEs based on OSRS, RSS, ORSS, and DRSS schemes. We also compare the estimators based on imperfect RSS (IRSS) schemes. It is worth mentioning here that the BLUEs under ordered imperfect DRSS (OIDRSS) are better than their counterparts based on IRSS, ordered IRSS (OIRSS), and imperfect DRSS (IDRSS) methods. Moreover, for sensitivity analysis of the BLUEs, we calculate REs and REDs of the BLUEs under the assumption of normality when in fact the parent distribution follows a non normal symmetric distribution. It turns out that even under violation of normality assumptions, BLUEs of the intercept and the slope parameters are found to be unbiased with equal REs under each sampling scheme. It is also observed that the BLUEs under ODRSS are more efficient than the existing BLUEs.
AbstractList In this paper, we consider the best linear unbiased estimators (BLUEs) based on double ranked set sampling (DRSS) and ordered DRSS (ODRSS) schemes for the simple linear regression model with replicated observations. We assume three symmetric distributions for the random error term, i.e., normal, Laplace and some scale contaminated normal distributions. The proposed BLUEs under DRSS (BLUEs-DRSS) and ODRSS (BLUEs-ODRSS) are compared with the BLUEs based on ordered simple random sampling (OSRS), ranked set sampling (RSS), and ordered RSS (ORSS) schemes. These estimators are compared in terms of relative efficiency (RE), RE of determinant (RED), and RE of trace (RET). It is found that the BLUEs-ODRSS are uniformly better than the BLUEs based on OSRS, RSS, ORSS, and DRSS schemes. We also compare the estimators based on imperfect RSS (IRSS) schemes. It is worth mentioning here that the BLUEs under ordered imperfect DRSS (OIDRSS) are better than their counterparts based on IRSS, ordered IRSS (OIRSS), and imperfect DRSS (IDRSS) methods. Moreover, for sensitivity analysis of the BLUEs, we calculate REs and REDs of the BLUEs under the assumption of normality when in fact the parent distribution follows a non normal symmetric distribution. It turns out that even under violation of normality assumptions, BLUEs of the intercept and the slope parameters are found to be unbiased with equal REs under each sampling scheme. It is also observed that the BLUEs under ODRSS are more efficient than the existing BLUEs.
Author Brown, Jennifer
Moltchanova, Elena
Haq, Abdul
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SubjectTerms Best linear unbiased estimator
Economic models
Estimators
Mathematical models
Normality
Order statistics
Primary: 62D05; Secondary: 62F10
Ranked set sample
Regression
Regression analysis
Relative efficiency
Sampling
Sensitivity analysis
Simple linear regression model
Statistics
Symmetry
Title Improved best linear unbiased estimators for the simple linear regression model using double ranked set sampling schemes
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