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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Vydáno v:Communications in statistics. Theory and methods Ročník 45; číslo 12; s. 3541 - 3561
Hlavní autoři: Haq, Abdul, Brown, Jennifer, Moltchanova, Elena
Médium: Journal Article
Jazyk:angličtina
Vydáno: Philadelphia Taylor & Francis 17.06.2016
Taylor & Francis Ltd
Témata:
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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Shrnutí: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.
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ISSN:0361-0926
1532-415X
DOI:10.1080/03610926.2014.904350