Estimation Of Finite Population Mean Research Articles

Some Exponential Type Predictive Estimators of Finite Population Mean in Two-Phase Sampling

This study is designed for predictive estimation of finite population mean in two phase sampling using two auxiliary variables. Two phase exponential ratio type estimator and exponential chain ratio type estimator are proposed under predictive approach suggested by Bahl & Tuteja (1991). The expressions of bias and mean square error of both suggested estimators have been carried out for theoretical comparison. The numerical study on real life data sets as well as simulation study has been conducted to examine the performance of suggested estimators. Finally, it is demonstrated that the suggested exponential ratio estimators are more efficient than competitive estimators in support of numerical and simulation study as well.

Estimation of finite population mean using two auxiliary variables under stratified random sampling

Abstract This paper addresses the problem of an alternative approach to estimating the population mean of the study variable with the help of the auxiliary variable under stratified random sampling. The properties of the suggested estimator have been studied under large sample approximation. It has been demonstrated that the suggested estimator is more efficient than other considered estimators. To judge the merits of the proposed estimator, an empirical study has been carried out to support the present study.

A simulation study: new optimal estimators for population mean by using dual auxiliary information in stratified random sampling

ABSTRACT Recently, Haq et al. [A new estimator of finite population mean based on the dual use of the auxiliary information. Commun Stat Theory Methods. 2017;46(9):4425–4436] utilized the dual auxiliary information under simple random sampling only. Motivated by their idea, we initiated the dual use of auxiliary variable under a stratified random sampling scheme. Dual use of auxiliary variable consists: (1) the original auxiliary information and (2) the ranked auxiliary information. We proposed new optimal exponential-type estimators for the estimation of the finite population mean. Mathematical properties such as bias and mean squared error of the proposed estimators are derived. Monte Carlo simulation studies are included to successfully validate the theoretical results. Moreover, the applicability of the proposed estimators is highlighted through empirical interpretation with the help of a real-life data set. It is clearly identified from the numerical results that our proposed estimators are more efficient over the competitors.

Improved estimation of finite population mean in two-phase sampling with subsampling of the nonrespondents

ABSTRACT Improved chain-ratio estimators for the population mean based on two-phase sampling are proposed when the study variable and two auxiliary variables comprise non-response. Auxiliary information is available for the first variable and not available for the second variable. Their biases and mean square errors are estimated under large sample approximation. Their efficiencies are compared with Hansen and Hurwitz’s estimator, the ratio and regression estimators for a single auxiliary variable, and Singh and Kumar’s estimators for two auxiliary variables. Empirical evaluations using both model-based and design-based simulations show that these estimators perform better than Hansen and Hurwitz’s estimator, the ratio and the regression estimators, and Singh and Kumar’s estimator.

A new efficient class of estimators of finite population mean in simple random sampling

The crux of the paper is to develop a very general class of estimators for population mean $$ \bar{Y} $$ of the study variable $$ y $$ using information on auxiliary variable $$ x $$ in simple random sampling. It has been shown that a large number of known and unknown estimators are members of the suggested class of estimators. Expressions of bias and mean squared errors of the proposed class of estimators have been obtained under large sample approximation. Asymptotic optimum estimator (AOE) in the proposed class of estimators has been obtained with its mean squared error formula. An empirical study is carried out to demonstrate the superiority of the members of the proposed class of estimators over existing estimators.

A Ratio and Ratio Exponential Estimator for Finite Population Mean in Case of Post-Stratification

A Ratio and Ratio Exponential Estimator for Finite Population Mean in Case of Post-Stratification

New class of exponential estimators for finite population mean in two-phase sampling

This paper suggests a new family of exponential estimators in the two-phase sampling using the information of an auxiliary attribute. Theoretically, we obtain the mean square error (MSE) for these estimators. We compare the MSE equations of the proposed exponential ratio families of estimators with the MSE equations of the ratio estimators in literature. As a result of these comparisons, we observe that the proposed families of estimators give more efficient results than the estimators in literature for the determined conditions obtained in theory. In addition, these theoretical results are supported by an application with original data sets.

Some calibration estimators for finite population mean in two-stage stratified random sampling

In the present article, an effort has been made to develop calibration estimators of the population mean under two-stage stratified random sampling design when auxiliary information is available at primary stage unit (psu) level. The properties of the developed estimators are derived in-terms of design based approximate variance and approximate consistent design based estimator of the variance. Some simulation studies have been conducted to investigate the relative performance of calibration estimator over the usual estimator of the population mean without using auxiliary information in two-stage stratified random sampling. Proposed calibration estimators have outperformed the usual estimator without using auxiliary information.

Efficient Class of Estimators for Finite Population Mean using Auxiliary Information in Two-Occasion Successive Sampling

In the case of sampling on two occasions, a class of estimators is considered which uses information on the first occasion as well as the second occasion in order to estimate the population means on the current (second) occasion. The usefulness of auxiliary information in enhancing the efficiency of this estimation is examined through the class of proposed estimators. Some properties of the class of estimators and a strategy of optimum replacement are discussed. The proposed class of estimators were empirically compared with the sample mean estimator in the case of no matching. The established optimum estimator, which is a linear combination of the means of the matched and unmatched portions of the sample at the current occasion, was empirically compared with the proposed class of estimators. Mutual comparisons of the proposed estimator were carried out. Suitable recommendations are made to the survey statistician for practical applications.

Estimation of finite population mean for a sensitive variable using dual auxiliary information in the presence of measurement errors.

In this study, we propose a new improved estimator of population mean for the sensitive variable in the presence of measurement error under simple and stratified random sampling. This estimator accounts the auxiliary information as well as the ranks of the auxiliary variable. From theoretical and numerical studies it is shown that a new improved estimator performs better than the existing estimators under study.

Ratio estimation of the mean under RRT models

In this paper, we introduce a ratio estimator for finite population mean in the context of optional RRT models. We discuss the Bias and the Mean Square Error (MSE) of our proposed ratio estimator, correct up to first order of approximation, and present its comparison with some other estimators. A simulation study is also conducted to validate the theoretical results. Both the theoretical and the empirical results show that the proposed ratio estimator is more efficient than the competing estimators.

A generalized class of estimators under two-phase stratified sampling for non response

In this paper, we propose a generalized class of estimators for finite population mean using two auxiliary variables in two-phase stratified sampling for non response. We identify 17 estimators as special cases of the proposed class of estimators. Expressions for the bias and mean squared error (MSE) of estimators are obtained up to first order of approximation. A data set is used for efficiency comparisons.

A new estimator for mean under stratified random sampling

In this paper, we have proposed an estimator of finite population mean in stratified random sampling. The expressions for the bias and mean square error of the proposed estimator are obtained up to the first order of approximation. It is found that the proposed estimator is more efficient than the traditional mean, ratio, exponential, regression, Shabbir and Gupta (in Commun Stat Theory Method 40:199–212, 2011) and Khan et al. (in Pak J Stat 31:353–362, 2015) estimators. We have utilized four natural and four artificial data sets under stratified random sampling scheme for assessing the performance of all the estimators considered here.

Estimation of Finite Population Mean by Using Minimum and Maximum Values in Stratified Random Sampling

Estimation of Finite Population Mean by Using Minimum and Maximum Values in Stratified Random Sampling

A Class of Hartley-Ross-Type Estimators for Population Mean in Adaptive and Stratified Adaptive Cluster Sampling

In this article, we propose a class of Hartley-Ross-type unbiased estimators of finite population mean under adaptive cluster sampling and stratified adaptive cluster sampling. The estimators utilize information on known parameters of the auxiliary variable. The variances of proposed class of unbiased estimators are obtained up to first degree of approximation. Proposed estimators are more efficient than the usual mean estimator, ratio, and modified ratio estimators in adaptive cluster sampling and stratified adaptive cluster sampling under certain realistic conditions. Simulation study considering different populations is carried out to support the theoretical findings.

Estimation of mean using generalized optional scrambled responses in the presence of non-sensitive auxiliary variable

In this article, the estimation of finite population mean of a sensitive variable based on generalized optional scrambled responses collected using a randomization device is presented under single sample approach. The estimator is then improved by using non-sensitive auxiliary information. Some special cases and privacy protection for proposed model has also been discussed. Simulation studies are conducted to evaluate the proposed device.

Estimation of finite population mean in stratified sampling using scrambled responses in the presence of measurement errors

ABSTRACTThis study focuses on the estimation of population mean of a sensitive variable in stratified random sampling based on randomized response technique (RRT) when the observations are contaminated by measurement errors (ME). A generalized estimator of population mean is proposed by using additively scrambled responses for the sensitive variable. The expressions for the bias and mean square error (MSE) of the proposed estimator are derived. The performance of the proposed estimator is evaluated both theoretically and empirically. Results are also applied to a real data set.

Almost Unbiased Ratio cum Product Estimator for Finite Population Mean with Known Median in Simple Random Sampling

Introduction: In sampling theory, different procedures are used to obtain the efficient estimator of the population mean. The commonly used method is to obtain the estimator of the population mean is simple random sampling without replacement when there is no auxiliary variable is available. There are methods that use auxiliary information of the study characteristics. If the auxiliary variable is correlated with study variable, number of estimators are widely available in the literature.Objective: This study deals with a new ratio cum product estimator is developed for the estimation of population mean of the study variable with the known median of the auxiliary variable in simple random sampling.Materials and Methods: The bias and mean squared error of proposed estimator are derived and compared with that of the existing estimators by analytically and numerically.Results: The proposed estimator is less biased and mean squared error is less than that of the existing estimators and from the numerical study, under some known natural populations, the bias of proposed estimator is approximately zero and the mean squared error ranged from 6.83 to 66429.21 and percentage relative efficiencies ranged from 103.65 to 2858.75.Conclusion: The proposed estimator under optimum conditions is almost unbiased and performs better than all other existing estimators.Nepalese Journal of Statistics, 2017, Vol. 1, 1-14

An Improved Family of Estimators of Finite Population Mean Using Information on an Auxiliary Variable in Sample Surveys

AbstractIn this paper we have suggested a family of estimators of the population mean using auxiliary information in sample surveys. The bias and mean squared error of the proposed class of estimators have been obtained under large sample approximation. We have derived the conditions for the parameters under which the proposed class of estimators has smaller mean squared error than the sample mean, ratio, product, regression estimator and the two parameter ratio-product-ratio estimators envisaged by Chami et al (2012). An empirical study is carried out to demonstrate the performance of the proposed class of estimators over other existing estimators.

Dual to Ratio and Product Type Exponential Estimators of Finite Population Mean in Double Sampling for Stratification

Dual to Ratio and Product Type Exponential Estimators of Finite Population Mean in Double Sampling for Stratification