Ranked Set Sampling Method And Parameter Estimation Based On This Method

As a basis of inferring population from individual ,sampling theory are playing more and more important roles in the reality.Sampling theory is corresponding to sampling method.With the development of the society,traditional sampling method cann`t satisfy the practice need of the human being any longer.In recent years,a new sampling method has been developed which is called ranked set sampling(RSS).When observations are costly or time-consuming but the ranking of the observations without actual measurement can be done relative easily,RSS can be employed instead of simple random sampling(SRS) to gain more information.It has many applications in biology,agricultural and environmental studies since its emergement. From a statistic point of view,an RSS sample should always contain more information than an SRS sample,since an RSS sample contains not only the information carried by the quantified observations but also the information provided by the judgment ranking.This is definitely true.It is proved that the Fisher information matrix from an RSS sample is the sum of the information matrix from an SRS sample and an additional non-negative definite matrix.What`s more,as far as the location-scale population is concerned,we show that the Fisher information matrix from an RSS sample is independent of the location parameter and is inversely proportional to the scale parameter.The maximum likelihood estimation(MLE) from an RSS sample is consistent an asymptotically normal and more efficient than its counterpart from an SRS sample. Based on this MLE the confidence intervals of the parameters can be constructed,and at the same confidence level the average length of the confidence interval from an RSS sample is short than its counterpart from an SRS sample.Much research had been developed about the parameters` best linear unbiased estimation(BLUE).On this basis,We study the parameters best linear invariant estimation(BLIE) of the location-scale family,The comparation between the BLUE and BLIE from an RSS sample shows that the former is better in the sense of mean square error.