Study On Ratio Estimators And Unequal Probabilities Sampling Design With Fixed Sample Size

In the sampling surveys, we can reduce the difficulty of the survey and obtain a more representative sample by using auxiliary information effectively. In addition, the new estimator can also be constructed by the auxiliary information, which can reduce the error of the estimator, and correct the deviation between the estimator and the research variable. This paper constructs a chain product estimator in simple random sampling without replacement and a chain ratio-product type estimator in systematic sampling, using auxiliary information. And three kinds of unequal probability sampling design of fixed sample size are improved. The new designs are more convenient and stable to obtain a sample than the original designs, and the accuracy is also improved when the correlation between the study variables and the auxiliary information is high.First, in sampling surveys, the precision of the estimators can be increased by using properly auxiliary information. When the auxiliary variable X and the interest variable Y showed a negative correlation relationship, the traditional method is to use the product estimation for population mean. The chapter presents a chain product estimation for population mean, and its mean square error(MSE) is obtained. We prove that the chain product estimator is more efficient than the traditional product estimator under certain conditions. In addition, this result is supported by an application with original data.Second, This chapter proposed a chain ratio-product type estimator for estimating the finite population mean in systematic sampling, using two auxiliary variables. The estimator is not an unbiased estimator of the population mean, but the precision of proposed estimator has been enhanced. The expressions of bias and mean square error(MSE) have been derived, to the first degree of approximation. Besides, we have found some theoretical conditions make the precision of suggested estimator over other known estimator in systematic sampling. Finally, we give a numerical example.Third, in this chapter, inspired by conditional collocated sampling, the Poisson sample in CP, 2PπPS and AP sampling is replaced with a collocated sample. Becauseof the excellent properties of collocated sample. Besides, the numerical study is carried out, and the numerical simulation method of calculating the inclusion probabilities is presented.