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.

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.

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.

Geochemical Mapping:With Special Emphasis on Analytical Requirements

More than 40 national and regional geochemical mapping projects in the world carried out from 1973 to 1988 do not conform to common standards. In particular they have many analytical deficiencies. In the period 1988 to 1992, the International Geochemical Mapping project （Project 259 of UNESCO＇s IGCP Program） prepared recommendations designed to standardize geochemical mapping methods. The analytical requirements are an essential component of the overall recommendations. They included the following： 71 elements should be analyzed in future mapping projects; the detection limits of trace and ultratrace elements must be lower than the corresponding crustal abundances; and the Chinese GSD and Canadian STSD standard sample series should be used for the correlation of global data. A proposal was also made to collect 5000 composite samples, at very low sampling densities to cover the whole Earth＇s land surface. In 1997 an IUGS Working Group on Global Geochemical Baselines was formed to continue the work which began with IGCP 259. From 1997 up to now, new progress has been made especially in China and FOREGS countries under the aegis of this working group, including the study of suitable sampling media, development of a multi-element analytical system, new proficiency test for selection of competent laboratories and role of wide-spaced mapping in mineral exploration. One of the major problems awaiting solution has been the inability of many laboratories to meet the IGCP recommendations to generate high quality geochemical maps. Fortunately several laboratories in China and Europe have demonstrated an ability to meet the requirements and they will be well placed to render technical assistance to other countries.

The application of the entropy-based statistic for genomic association study of QTL

An entropy-based statistic TpE has been proposed for genomic association study for disease-susceptibility locus. The statistic TpE may be directly adopted and/or extended to quantitative-trait locus （QTL）mapping for quantitative traits. In this article, the statistic TpE was extended and applied to quantitative trait for association analysis of QTL by means of selective genotyping. The statistical properties （the type I error rate and the power） were examined under a range of parameters and population-sampling strategies （e.g., various genetic models, various heritabilities, and various sample-selection threshold values） by simulation studies. The results indicated that the statistic TpE is robust and powerful for genomic association study of QTL. A simulation study based on the haplotype frequencies of 10 single nucleotide polymorphisms （SNPs） of angiotensin-I converting enzyme genes was conducted to evaluate the performance of the statistic TPE for genetic association study.

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.

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.

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.