Estimation of Simple Linear Regression Model Using L Ranked Set Sampling

In this article, L ranked-set sampling (LRSS) is used to estimate a simple linear regression model. We show that the estimated regression model based on LRSS is highly efficient compared to the estimators based on simple random sampling, Extreme ranked set sampling and ranked set sampling. Monte Carlo experiments are performed to assess the accuracy and the robustness of the LRSS estimates. The results are illustrated by an example.

[1]  Hani M. Samawi,et al.  Estimating the Population Mean Using Extreme Ranked Set Sampling , 1996 .

[2]  N. Draper,et al.  Applied Regression Analysis , 1966 .

[3]  Zehua Chen Ranked-set sampling with regression-type estimators , 2001 .

[4]  Hassen A. Muttlak,et al.  Parameters Estimation in a Simple Linear Regression Using Rank Set Sampling , 1995 .

[5]  Zehua Chen,et al.  Efficient regression analysis with ranked-set sampling. , 2004, Biometrics.

[6]  M. Nadel,et al.  Scott sentences and admissible sets , 1974 .

[7]  G. McIntyre,et al.  A method for unbiased selective sampling, using ranked sets , 1952 .

[8]  M. Makkai,et al.  An “admissible” generalization of a theorem on countable ∑11 sets of reals with applications , 1977 .

[9]  Amjad D. Al-Nasser L Ranked Set Sampling: A Generalization Procedure for Robust Visual Sampling , 2007, Commun. Stat. Simul. Comput..

[10]  Stephen L. Rathbun,et al.  The Population Dynamics of a Long-Lived Conifer (Pinus palustris) , 1988, The American Naturalist.

[11]  Ganapati P. Patil,et al.  Relative precision of ranked set sampling: A comparison with the regression estimator , 1993 .

[12]  Cameron E. Freer Models with high Scott rank , 2008 .

[13]  J. Barwise Admissible Sets and Structures: An Approach to Definability Theory , 1976 .

[14]  Chunming Zhang,et al.  Ranked Set Sampling: Theory and Applications , 2005, Technometrics.

[15]  P. Yu,et al.  Regression estimator in ranked set sampling. , 1997, Biometrics.

[16]  Michael Makkai,et al.  An example concerning Scott heights , 1981, Journal of Symbolic Logic.

[17]  Michael D. Morley The Number of Countable Models , 1970, J. Symb. Log..