The Efficiency Of Moving Extremes Ranked Set Sampling Design For Statistical Inference For Two Classes Of Models

The most common sampling approach for collecting data from a population with the goal of making inferences about unknown features of the population is a simple random sampling(SRS).The theory derived from SRS has been quite perfect and mature so far But in practice,it is impossible to measure a large number of samples on the one hand,which is limited by the scale or the cost of the experiment;on the other hand,the actual measurement of the sample may be have some difficulties or destructive,at this time we need to take other sampling methods.Initially the concept of Ranked Set Sampling(RSS)was introduced by McIntyre(1952)as a process of increasing the precision of the sample mean as an estimator of population mean.Especially when the interest variables are not easy to quantify and easy to ranking,the advantages of RSS are more obvious.Because of its high efficiency,it is now widely used in agriculture,environment and medicine.In order to reduce the error of ranking and keep optimality inherited in the original RSS procedure.Al-odat and Al-saleh(2000)introduced the concep-t of varied set size RSS,which is coined here as Moving Extreme Ranked Set SampIing(MERSS).There has also been some study of parametric inference in MERSS.Al-saleh and Hadhrami(2003a)studied estimation of location parame-ter for symmetric distribution in the case of normal distribution under MERSS.Al-saleh and Hadhrami(2003b)studied estimation of scale parameter for the exponential distribution under MERSS.Chen et al.(2019)studied estimation of parameters for Pareto distributions under MERSS.In this paper.We are interested in studying the efficiency of parameter estimation for the location-scale family and the simple linear regression with replicated observations under MERSS.The dissertation is devoted to the fol-lowing researches:(1)MERSS is considered for maximum likelihood estimators(MLEs)the parameters from the Logistic distribution.We respectively prove the existence and uniqueness of MLEs of the location parameter and the scale parameter from this distribution under SRS and MERSS.The Fisher information number and Fisher information matrix under the two samplings are respectively comput-ed.The MLEs under MERSS are compared to the corresponding ones under MERSS are significantly more efficient than the ones under SRS.(2)MERSS is considered for the Fisher information matrix for the location-scale family.The Fisher information matrix for this model are respectively derived under SRS and MERSS.In order to give more insight into the per-formance of MERSS with respect to SRS,the Fisher information matrix for the extreme-value data and the normal data are respectively computed under the two samplings.The numerical results show that MERSS provides more information than SRS in parametric inference.(3)MERSS is considered for the best linear unbiased estimations(BLUEs)for the simple linear regression model with replicated observations.The BLUE-under MERSS are show to be markedly more efficient for normal data when compared with the BLUEs under SRS.(4)MERSS is considered for the Fisher information matrix for the Simple linear regression model with replicated observations.The SRS Fisher infor-mation matrix and the MERSS Fisher information matrix for this model are respectively derived.In order to give more insight into the performance of MERSS with respect to SRS,the information matrix for the extreme-value da-ta and the normal data are respectively computed under the two samplings.The numerical results show that MERSS provides more information than SRS in parametric inference.