Best linear unbiased estimators of parameters of a simple linear regression model based on ordered ranked set samples. (English) Zbl 1169.62051
Summary: As an alternative to estimation based on a simple random sample (BLUE-SRS) for the simple linear regression model, E. Moussa-Hamouda and F. C. Leone [Technometrics 16, 441–446 (1974; Zbl 0285.62043)] discussed the best linear unbiased estimators based on order statistics (BLUE-OS), and showed that BLUE-OS are more efficient than BLUE-SRS for normal data. Using ranked set sampling, M. C. M. Barreto and V. Barnett [Best linear unbiased estimators for the simple linear regression model using ranked set sampling. Environ. Ecol. Stat. 6, 119–133 (1999)] derived the best linear unbiased estimators (BLUE-RSS) for simple linear regression models and showed that BLUE-RSS is more efficient for the estimation of the regression parameters (intercept and slope) than BLUE-SRS for normal data, but not so for the estimation of the residual standard deviation in the case of small sample size. As an alternative to RSS, this paper considers the best linear unbiased estimators based on order statistics from a ranked set sample (BLUE-ORSS) and shows that BLUE-ORSS is uniformly more efficient than BLUE-RSS and BLUE-OS for normal data.
MSC:
| 62H12 | Estimation in multivariate analysis |
| 62J05 | Linear regression; mixed models |
| 62G30 | Order statistics; empirical distribution functions |
| 62Q05 | Statistical tables |
Citations:
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