Estimators For The Population Mean In The Case Of Missing Data And Strict ?ps Sampling With Sample Size N=2

In the actual investigation and study,it is often necessary to know overall characteristics of the overall care indicators,such as,population total or mean etc.Although the estimate of mean value is simple,the accompanied by the estimation accuracy is not high,when there are missing data,and even more so.In order to improve the existing population parameter estimator,improving the estimation accuracy is a further research topic.A large number of documents can improve the survey precision by use of auxiliary information.Where there is known auxiliary information,available,high precision estimation of unequal probability sampling design,the n=2 strict ?ps sampling designis an unequal probability sampling.Typical strict ?ps samples are designed to how toimply the n=2 the design and calculate the first-order inclusion and second-orderinclusion problem is the main research direction of this paper.First of all,in the practical investigation,we can often get auxiliary information which is known,and it usually and research variables were positively correlated.The rational use of auxiliary information,such as the overall mean value and variation coefficient,coefficient of kurtosis,coefficient of Skewness,correlation coefficient and so on,can improve the accuracy of the estimated values play a great help.The sampling survey often will inevitably encounter the missing data,such as records of personal carelessness,and refuse to disclose information.This is the case with missing data based on the coefficient of kurtosis,skewness of the auxiliary variables and put forward a series of overall mean estimator.Using the taylor series expansion for proposed estimators of the mean square error and bias.The mean square error as the standard precision characterization,it theoretically explains the merits of the proposed estimation and estimation have been obtained,the premise is better than estimated,and based on the formula and the effectiveness of these estimators is verified by Monte Carlo simulation.Secondly,inspired by Deshpande and Prabhu(1982)design idea,this paperconstructs a new n=2 strict ?ps sampling design.When the auxiliary unit size,the newdesign is not only easy to implement,but also the first-order and second-order inclusion probability calculation is simple.In addition,can also obtain H-T estimation the amount of a non-negative variance estimation.Designed by the numerical comparison and classic ?ps sampling design,we found that the proposed method has the potential applicationvalue.Finally,proposed a new design of the strict ?ps stratified sampling when n=2,so borrowed the idea,set up the theory of the strict ?ps stratified sampling when n=2 ineach stratum,and evaluated its precision based on the actual data set.