Parametric estimation for the simple linear regression model under moving extremes ranked set sampling design

Cost effective sampling design is a major concern in some experiments especially when the measurement of the characteristic of interest is costly or painful or time consuming.Ranked set sampling(RSS)was first proposed by McIntyre[1952.A method for unbiased selective sampling,using ranked sets.Australian Journal of Agricultural Research 3,385-390]as an effective way to estimate the pasture mean.In the current paper,a modification of ranked set sampling called moving extremes ranked set sampling(MERSS)is considered for the best linear unbiased estimators(BLUEs)for the simple linear regression model.The BLUEs for this model under MERSS are derived.The BLUEs under MERSS are shown to be markedly more efficient for normal data when compared with the BLUEs under simple random sampling.

Log-logistic parameters estimation using moving extremes ranked set sampling design

In statistical parameter estimation problems,how well the parameters are estimated largely depends on the sampling design used.In the current paper,a modification of ranked set sampling(RSS)called moving extremes RSS(MERSS)is considered for the estimation of the scale and shape parameters for the log-logistic distribution.Several traditional estimators and ad hoc estimators will be studied under MERSS.The estimators under MERSS are compared to the corresponding ones under SRS.The simulation results show that the estimators under MERSS are significantly more efficient than the ones under SRS.

Double Moving Extremes Ranked Set Sampling Design

The traditional simple random sampling(SRS)design method is inefficient in many cases.Statisticians proposed some new designs to increase efficiency.In this paper,as a variation of moving extremes ranked set sampling(MERSS),double MERSS(DMERSS)is proposed and its properties for estimating the population mean are considered.It turns out that,when the underlying distribution is symmetric,DMERSS gives unbiased estimators of the population mean.Also,it is found that DMERSS is more efficient than the SRS and MERSS methods for usual symmetric distributions(normal and uniform).For asymmetric distributions considered in this study,the DMERSS has a small bias and it is more efficient than SRS for usual asymmetric distribution(exponential)for small sample sizes.

Maximum Likelihood Estimator of the Location Parameter under Moving Extremes Ranked Set Sampling Design

Cost effective sampling design is a problem of major concern in some experiments especially when the measurement of the characteristic of interest is costly or painful or time consuming.In the current paper,a modification of ranked set sampling(RSS)called moving extremes RSS(MERSS)is considered for the estimation of the location parameter for location family.A maximum likelihood estimator(MLE)of the location parameter for this family is studied and its properties are obtained.We prove that the MLE is an equivariant estimator under location transformation.In order to give more insight into the performance of MERSS with respect to(w.r.t.)simple random sampling(SRS),the asymptotic efficiency of the MLE using MERSS w.r.t.that using SRS is computed for some usual location distributions.The relative results show that the MLE using MERSS can be real competitors to the MLE using SRS.

Best Linear Unbiased Estimators of Location and Scale Ranked Set Parameters under Moving Extremes Sampling Design

In the current paper,the best linear unbiased estimators(BLUEs)of location and scale parameters from location-scale family will be respectively proposed in cases when one parameter is known and when both are unknown under moving extremes ranked set sampling(MERSS).Explicit mathematical expressions of these estimators and their variances are derived.Their relative efficiencies with respect to the minimum variance unbiased estimators(MVUEs)under simple random sampling(SRS)are compared for the cases of some usual distributions.The numerical results show that the BLUEs under MERSS are significantly more efficient than the MVUEs under SRS.

Fisher Information in Moving Extreme Ranked Set Sampling with Application to Parameter Estimation

In statistical parameter estimation problems,how well the parameters are estimated largely depends on the sampling design used.In the current paper,a modification of ranked set sampling called moving extremes ranked set sampling(MERSS)is considered for the Fisher information matrix for the location-scale family.The Fisher information matrix for this model are respectively derived under simple random sampling and MERSS.In order to give more insight into the performance of MERSS with respect to simple random sampling,the Fisher information matrix for usual locationscale distributions are respectively computed under the two sampling.The numerical results show that MERSS provides more information than simple random sampling in parametric inference.