Optimal Estimation Of The Mean Under The Optimal Sampling Design And Other Related Studies

How to obtain samples that are representative or contain more population information is an important components of sampling design theory.In order to obtain more samples containing effective information,scholars at home and abroad have proposed many new sampling methods.Moving extremes ranked set sampling(MERSS)is one of them.MERSS further considered some practical conditions due to the constraints of funds and time.It is appropriate for situations in which quantification of sampling units is difficult but ranking of the units is easy.In sample survey,estimation of mean is one of the key issues relating to the field of agriculture,environment,economics and medicine.The literature on survey sampling describes two directions for the estimation of mean.One is to estimate the mean directly through the sample mean without utilizing information of auxiliary variables.The other is to estimate the mean indirectly by using regression estimation and other methods with utilizing information of auxiliary variables.Since effective sampling methods can improve the efficiency of sampling,studying the estimation of mean in good sampling design is helpful to improve the accuracy of estimation,the estimation of the mean and its related studies based on optimal MERSS are discussed in this dissertation.The main research parts of this dissertation areas follows:(i)The regression estimators of the mean and its optimal properties under MERSS when auxiliary information μ_X known are studied.The first simple random sampling(SRS)sample is used to estimate μ_X when μ_X unknown,the regression estimator of the mean and its optimal properties under SRS-MERSS double sampling are studied.The results show that the regression estimator under MERSS is superior to the one under SRS when μ_X known,and the regression estimator under SRS-MERSS double sampling is superior to the one under SRS-SRS double sampling when μ_X unknown.(ii)The double moving extremes ranked set sampling(DMERSS)is proposed.The estimation of the mean and its optimal properties under DMERSS are studied.The results show that DMERSS sample are more efficient than MERSS sample and SRS sample when the population distribution is symmetric.(iii)The first moving extremes ranked set sample is used to estimate μ_X whenμ_X unknown,the regression estimator of the mean and its optimal properties under DMERSS are studied.The results show that the regression estimator under DMERSS is superior to the one under SRS-MERSS and SRS-SRS double sampling.(iv)In order to find a better sampling method to improve the efficiency of sampling,the ordered moving extremes ranked set sampling(OMERSS)is proposed.The estimation of the mean and its optimal properties under OMERSS are studied.The results show that OMERSS sample are more efficient than SRS sample when the population distribution is symmetric.(v)The maximum likelihood estimators(MLEs)of parameters β and λ in the Exponential-Poisson(EP)distribution under ranked set sampling(RSS)and MERSS respectively.The results show that the MLEs under RSS or MERSS are significantly more efficient than the ones under SRS respectively.(vi)Fisher information in the corresponding samples about the parameter θfrom Inverse Rayleigh(IR)distribution under SRS,RSS and MERSS are respectively studied.And some optimal estimators of θ are constructed under simple random sample,ranked set sample and moving extremes ranked set sample respectively.The results show that these estimators under RSS or MERSS are significantly more efficient than the ones under SRS,respectively.