For estimating the mean of a finite population using information on p auxiliary characters x1, ···, xp1 a class of ratio type estimators is considered. For any function h(u1, ···, up) = h(u) where , the ratio of the simple random sample mean and the population mean of the character xi, such that h(e) = 1, ei = 1, i = 1, ···, p, and such that it satisfies the conditions (1), (2) and (3) of Section 3, the estimator considered is . Asymptotic expressions for the bias and the variance of the estimator are obtained and it has been shown that ratio estimators of the form are asymptotically no more efficient than the regression estimator.

A Generalized Estimator for the Mean of a Finite Population Using Multi-Auxiliary Information

https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=6189&context=rtd

Some ratio-type estimators based on two or more auxiliary variables

Summary. We consider a class of ratio-product estimators for estimating a finite population mean. The asymptotically optimum estimator in the class is identified, along with its approximate mean-square error. This estimator requires prior knowledge of the parameter C = pCy/Cx, where p is the correlation coefficient between the study variate y and the auxiliary variate x, and Cy and Cx are coefficients of variation of y and x respectively. If C is unknown in advance, then it can be replaced by its consistent estimate 0, with the resulting estimator known as an 'estimator based on the estimating optimum'. It is shown that, to the first order of approximation, both estimators have the same mean-square error, and that they are generally more efficient than the usual ratio and product estimators.

On linear regression and ratio–product estimation of a finite population mean

This paper presents exponential ratio and product estimators for estimating finite population mean using auxiliary information in double sampling and analyzes their properties. These estimators are compared for their precision with simple mean per unit, usual double sampling ratio and product estimators. An empirical study is also carried out to judge the merits of the suggested estimators.

/pdf/modified-exponential-ratio-and-product-estimators-for-finite-3zsohyib5f.pdf

Modified Exponential Ratio and Product Estimators for Finite Population Mean in Double Sampling

SUMMARY For estimating the mean of a finite population using information on an auxiliary variable, a class of estimators is defined as a function of the ratio of sample mean to population mean and the ratio of sample variance to population variance of the auxiliary variable. Asymptotic expressions for bias and mean squared error are obtained. A condition is given for the minimum mean squared error of estimators of this class to be smaller than those which use only the ratio of sample mean to population mean of the auxiliary variable.

A class of estimators of the population mean in survey sampling using auxiliary information

An Estimator Using Auxiliary Information in Sample Serveys

Summary

A two-phase sampling estimator of the ratio-type for estimating the mean Ȳ of a finite population, has been considered where the value of ρCy/Cx can be guessed or estimated in advance. Here Cy and Cx denote respectively the coefficients of variation of the characteristic under study, y, and the auxiliary characteristic x and ρ denotes the coefficient of correlation between y and x. When the value of ρCy/Cx is guessed or estimated exactly, the estimator has a smaller large-sample variance compared with either an ordinary ratio estimator or an ordinary linear regression estimator in two-phase sampling in the case where the first-phase sample is drawn independently from the second-phase sample. If the sample at the second phase is a subsample of the first-phasse sample, the estimator has variance equal to that of the linear regression estimator. The largest value of the difference between the assumed value and the actual value of ρCy/Cx has been obtained so as not to result in the variance of the estimator being larger than the variances of either an ordinary ratio estimator or an ordinary linear regression estimator.

Surendra K. Srivastava

Papers

A Generalized Estimator for the Mean of a Finite Population Using Multi-Auxiliary Information

An Estimator Using Auxiliary Information in Sample Serveys

A two‐phase sampling estimator in sample surveys