Estimators Of Finite Population Variance Research Articles

Robust Estimation of Variance Using Supplementary Information

This study introduces robust exponential ratio-type estimators for finite population variance, incorporating the minimum covariance determinant (M.C.D.) and minimum volume ellipsoid (M.V.E.) robust covariance matrices in the context of simple random sampling. We utilize a first-order approximation to derive expressions for the bias and mean square error (M.S.E.) of these proposed estimators. Through a comprehensive review of existing literature, it is evident that these robust estimators outperform other alternatives in terms of efficiency. Both the M.C.D. and M.V.E. methods are known for their resilience to outliers, making them particularly effective when such anomalies are present in the data. Simulation studies and empirical results consistently demonstrate that the proposed robust exponential ratio-type estimators yield lower mean square errors compared to traditional estimators under simple random sampling. Additionally, the efficiency of these estimators is further validated through simulated studies and real-world data sets. Theoretical analysis and numerical evidence collectively affirm that the proposed class of estimators consistently outperforms competing methods across various scenarios.

Enhanced Estimation of Population Variance under Simple Random Sampling with an Application to Real Data

In this paper, we present an enhanced class of estimators for finite population variance under simple random sampling that incorporates an auxiliary information. The equations for bias and mean square error of the proposed estimators are produced up to the first order of approximation. Some well-known estimators are found as a special case of the proposed estimators for suitably chosen values of the scalars. The effectiveness of the proposed estimators is calculated in relation to the existing estimators both theoretically and empirically using five real data sets. The empirical results exhibit the superiority of the suggested estimators over to the existing estimators in each population.. KEYWORDS :Auxiliary variable, Mean square error, Variance estimation, Class of estimators.

Efficient Classes of Robust Ratio Type Estimators of Mean and Variance in Adaptive Cluster Sampling

This paper proposes two classes of robust ratio type estimators of finite population mean and two classes of robust ratio type estimators of finite population variance using a single auxiliary variable under the adaptive cluster sampling design. Seven robust ratio type estimators have been developed from each class. The generalized expressions of bias and mean square error for each class have been derived up to the first order of approximation. The exact expressions of bias and MSE for all the developed estimators have been presented. Using simulation studies conducted in R programming, the high efficiency of all the developed estimators over similar existing estimators in adaptive cluster sampling has been demonstrated. . KEYWORDS :Adaptive cluster sampling, Classes of robust ratio type estimators, Hidden clustered data, Estimation of mean, Estimation of variance.

Improved estimators of population variance using robust measures in case of missing data

In this paper, an attempt has been made in proposing some improved estimators of finite population variance when random non-response is present in the study variable, on the estimators given by Sharma and Singh (2018). Four improved regression type estimators have been proposed using information on two auxiliary variables, one of which has missing values in the data, using two-phase sampling scheme. Different robust regression methods have been applied on the proposed techniques so as to improve the efficiency of the estimators in case of outliers. It has been observed that robust estimators are more efficient than the proposed ones under some conditions. All the proposed estimators are compared with existing estimators for different values of probability of non-response and the results are verified by using empirical and simulation studies.

An enhanced estimator of finite population variance using two auxiliary variables under simple random sampling

In this article, we have suggested a new improved estimator for estimation of finite population variance under simple random sampling. We use two auxiliary variables to improve the efficiency of estimator. The numerical expressions for the bias and mean square error are derived up to the first order approximation. To evaluate the efficiency of the new estimator, we conduct a numerical study using four real data sets and a simulation study. The result shows that the suggested estimator has a minimum mean square error and higher percentage relative efficiency as compared to all the existing estimators. These findings demonstrate the significance of our suggested estimator and highlight its potential applications in various fields. Theoretical and numerical analyses show that our suggested estimator outperforms all existing estimators in terms of efficiency. This demonstrates the practical value of incorporating auxiliary variables into the estimation process and the potential for future research in this area.

A new approach for estimating variance of a population employing information obtained from a stratified random sampling

In this article, we suggest an enhanced estimator for the estimation of finite population variance using twofold auxiliary variable under stratified random sampling. The numerical expressions for the bias and MSE are determined up to the first order of approximation. In order to effectively validate the theoretical findings, three actual data sets are included. Additionally, the application of the suggested estimators is demonstrated using a simulation study. Results of an empirical comparison among the suggested and existing estimators were investigated. To determine how good the suggested estimator, in comparison to the preliminary estimators, the MSE criterion is used. The suggested estimator has a smaller MSE and better PRE than existing estimators, according to numerical results utilizing actual data sets and a simulation analysis.

Estimation of Finite Population Variance Under Stratified Sampling in the Presence of Measurement Errors

ABSTRACT Measurement errors may significantly distort the properties of an estimator. In this paper, estimators of the finite population variance using the information on first and second raw moments of the study variable are developed under stratified random sampling that incorporate the variance of a measurement error component. Additionally, combined and separate estimators are also developed for estimating the finite population variance using supplementary information in terms of one or two auxiliary variables. An empirical study is carried out to study the effect of measurement error on the relative efficiencies of the proposed estimators.

Two new estimators of finite population variance under random non-response: An application

In this paper, an attempt has been made to study the estimation of finite population variance in simple random sampling without replacement (SRSWOR) in presence of non-response by proposing two estimators. The two estimators (dual to ratio and ratio cum dual to ratio type) have been proposed on the basis of availability and non-availability of auxiliary information. The properties such as bias and mean square error of the proposed estimators have also been studied up to first order of approximation. The proposed estimators are compared with some existing estimators and are also mutually compared. An empirical study, based on both vegetable crop data and simulated data, has been performed to find out the best estimator. It has been seen that out of the two proposed estimators, the ratio cum dual to ratio type estimator performed better than dual to ratio estimator.

On the Arithmetic Mean Estimators of a Family of Estimators of Finite Population Variance of Ratio Type

For many years, one of the difficult components of sampling theory has been the estimation of population characteristics, especially variance. The estimation of variability is very essential in many fields (Chemistry, Biology, Mathematics, and so on) to know how one quantity varies with respect to another quantity. This paper proposes arithmetic estimators of a group of ratio estimators for populations with finite variance. Using a Taylor series technique, the bias and MSE of the proposed estimators are determined up to the first order of approximation together with the efficiency conditions over existing estimators. The effectiveness of the proposed estimators in comparison to the current estimators is evaluated using a real-world data set. The empirical findings demonstrate that the suggested estimators outperform the current estimators taken into account in the study. Hence, these suggested estimators are recommended for use in real life scenario.

An Improved Estimator of finite Population Variance Using two Auxiliary Variable SRS

In the present study, we explore the problem of estimation of finite population variance in simple random sampling (without replacement) by utilizing information of two auxiliary variables. A ratio cum exponential estimator has been proposed and its properties are studied to the first degree of approximation. To demonstrate the efficiency, members of the proposed estimator as well as other existing estimators are compared to the usual unbiased estimator. To study the performance, a simulation study is undertaken for both real and artificial population using R software. The suggested estimator is found to be more efficient than other existing estimators in terms of having minimum MSE.

Improved Estimation of Finite Population Variance Using Dual Supplementary Information under Stratified Random Sampling

In this article, we propose an improved estimator for finite population variance based on stratified sampling by using the auxiliary variable as well as the rank of the auxiliary variable. Expressions for the bias and the mean square error of the estimators are derived up to the first order of approximation. Four real data sets are used to measure the performances of estimators. Moreover, a simulation study is also conducted to observe the efficiency of the proposed variance estimator. The theoretical and numerical results show that the proposed estimator under stratified random sampling is more efficient as compared to the existing estimators.

Some Improved Class of Ratio Estimators for Finite Population Variance with the Use of Known Parameters

Some Improved Class of Ratio Estimators for Finite Population Variance with the Use of Known Parameters

Some Optimal Estimators of Finite Population Variance Using Dual of Auxiliary Variable in the Presence of Random Non-Response

Some Optimal Estimators of Finite Population Variance Using Dual of Auxiliary Variable in the Presence of Random Non-Response

On the estimation of finite population variance for a mail survey design in the presence of non-response using new conventional and calibrated estimators

In this paper, we proposed new conventional unbiased and calibration estimators for estimating finite population variance for a Mail Survey Design characterized by the presence of non-response in practice. The properties of the proposed estimators are studied theoretically and numerically. Empirical studies were conducted using two each of existing and simulated data to illustrate the performance of proposed estimators over existing ones. The results of both theoretical and numerical comparison depicted the superiority of proposed estimators for estimating population variance for a Mail Survey Design characterized by non-response.

An improved generalized estimators for finite population variance of a study variable based on auxiliary information

The information on auxiliary variable has been shown to be relevant in selection and estimation of parameters to gain more precision in estimates of study variable. The transformation of this auxiliary information also aids increase efficiency of estimators. In this article, an improved mixed ratio-product-type exponential estimator is proposed and evaluated using information on auxiliary variable for population variance under simple random sampling. The mathematical expressions for bias and mean squared error (MSE) of the proposed estimator were derived up to first order of approximation. Using real data sets and Monte Carlo simulation study, the performance evaluation of the proposed estimator was considered and compared to the existing estimators. The results of the empirical and simulation studies show that the proposed estimator outperformed the existing estimators in term of MSE and PRE.

Generalized Estimators for Finite Population Variance Using Measurable and Affordable Auxiliary Character

In this paper, a generalized exponential-type estimator for estimating the population variance using measurable and affordable auxiliary character in single phase sampling has been proposed. Some special cases of the proposed generalized estimator with a = 1 and a = 2 have also been discussed. The expressions for the mean square error and bias of the proposed generalized estimator have been derived. The efficiency of the proposed generalized estimator has been compared theoretically with the existing estimators and the conditions under which the proposed estimators are better than some existing estimators have also been given. Numerical examples with five real data sets to compute MSEs and PREs were conducted to ascertain the efficiency of the proposed estimators over others and the results showed that both of the proposed estimators were more efficient than the estimators considered in literature. Thus, the estimator with perform better than the estimator with a = 1.

Estimation of finite population variance under stratified random sampling

In this paper, we develop estimators of the finite population variance using the information on the study variable’s first and second raw moments under stratified random sampling. In addition, both combined and separate estimators are also developed for estimating the population variance using supplementary information on a study variable and one or two auxiliary variables. The proposed estimators are compared with the existing estimators in terms of absolute bias and relative efficiency. Based on simulated and empirical studies, it is found that the proposed estimators may outperform the existing estimators.

Estimation of Finite Population Variance Under Stratified Sampling Technique

The efficiency of the study variable can be improved by incorporating the information from the known auxiliary variables. Usually two techniques ratio and regression estimation are used with the help of auxiliary information in different approaches to acquire the high precision of the estimators. Considering the very heterogeneous population to get the size of the sample it may be originating impossible to get a sufficiently accurate and precise estimate by taking the simple random sampling technique from the complete population. Occasionally taking sample issue may differ significantly in different part of the entire population. For example, under study population consists of people living in apartments, own homes, hospitals and prisons or people living in plain regions and hill regions so in such situations the stratified sampling is one of the most commonly used approach to get a representative sample in survey sampling from different cross units of the population. The present study is set out on the recommendation of generalized variance estimators for finite population variance incorporating stratified sampling scheme with the information of single and two transformed auxiliary variables. The expressions of bias and mean square error (MSE) are obtained for the advised exponential type estimators. The conditions are obtained for which the anticipated estimators are better than the usual estimator. An empirical and simulation study is conducted to prove the superiority of the recommended estimator.

Optimal estimation of population variance in the presence of random non-response using simulation approach

This paper introduces some new ratio- and difference-type estimators of the population variance in the presence of random non-response based on Searls (The utilization of a known coefficient of variation in the estimation procedure. J Am Stat Asso. 1964;59:1225–1226) philosophy. The proposed ratio- and difference-type estimators remain better than the estimators obtained by Ahmeda et al. (Estimation of finite population variance in presence of random non-response using auxiliary variables. Infr Mang Sci. 2005;16(2):73–82) in the presence of random non-response using auxiliary variables. The properties (bias and mean square error) of the proposed estimators presented were derived up to the first-order approximation using the Taylor series approach. Conditions for which the new estimators more efficient than other estimators considered in the study were also established. Numerical examples were conducted, and the results revealed that the proposed class of estimators is more efficient than existing estimators.

Ameliorated Class of Estimators of Finite Population Variance

A class of ratio estimators of finite population variance is proposed in this study. The properties of the proposed estimators have been derived using Taylor’s Series method up to first order of approximation. The efficiency conditions which are the mean square errors (MSEs) and percentage relative efficiency (PRE) of the proposed estimators over existing estimators have been established. The analytical illustration was also conducted to affirm the theoretical results. The results of the empirical study revealed that the proposed estimators are more efficient than the existing estimators considered in the study.