A Comparison of Estimators of Mean and Its Functions in Finite Populations (original) (raw)
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An Efficient Class of Estimators for Finite Population Mean Using Auxiliary Variable
Thailand Statistician, 2022
We have proposed a general class of estimators for population mean using auxiliary variable in simple random sampling. Our estimator contains various estimators from literature and many more can be developed from it. The expressions for bias and mean square error (MSE) are derived. It is found that the estimator in question is better than the other available alternatives. The Monte-Carlo simulation is carried out in various cases to show the validity of the estimator.
Hacettepe Journal of Mathematics and Statistics, 2016
This study proposes some ratio estimators of the population mean under simple random sampling schemes, in order to tackle the problem of low eciencies of some existing estimators. An improved exponential ratio estimator of the population mean under simple random sampling scheme and its bias and mean square error have been derived. Further propositions of a generalized form of the exponential ratio estimator of the population mean under simple random sampling scheme has also been made. The Bias and Mean Square Errors of these class of estimators have also been obtained. It is observed that some existing estimators are members of this class of estimators of population mean. Analytical and numerical results indicate that, the Asymptotic Optimal Estimator (AOE) of these proposed estimators of population mean using single auxiliary variable have been found to exhibit greater gains in eciencies than the classical regression estimators and other existing estimators in simple random sampling scheme.
On estimators of the mean of infinite dimensional data in finite populations
arXiv (Cornell University), 2023
The Horvitz-Thompson (HT), the Rao-Hartley-Cochran (RHC) and the generalized regression (GREG) estimators of the finite population mean are considered, when the observations are from an infinite dimensional space. We compare these estimators based on their asymptotic distributions under some commonly used sampling designs and some superpopulations satisfying linear regression models. We show that the GREG estimator is asymptotically at least as efficient as any of the other two estimators under different sampling designs considered in this paper. Further, we show that the use of some well known sampling designs utilizing auxiliary information may have an adverse effect on the performance of the GREG estimator, when the degree of heteroscedasticity present in linear regression models is not very large. On the other hand, the use of those sampling designs improves the performance of this estimator, when the degree of heteroscedasticity present in linear regression models is large. We develop methods for determining the degree of heteroscedasticity, which in turn determines the choice of appropriate sampling design to be used with the GREG estimator. We also investigate the consistency of the covariance operators of the above estimators. We carry out some numerical studies using real and synthetic data, and our theoretical results are supported by the results obtained from those numerical studies.
Efficient estimators for the population mean
Hacettepe Journal of Mathematics and …, 2009
M. Khoshnevisan, R. Singh, P. Chauhan, N. Sawan and F. Smarandache (A general family of estimators for estimating population mean using known value of some population parameter(s), Far East Journal of Theoretical Statistics 22, 181-191, 2007) introduced a family of estimators using auxiliary information in simple random sampling. They showed that these estimators are more efficient than the classical ratio estimator and that the minimum value of the mean square error (MSE ) of this family is equal to the MSE of the regression estimator. In this paper we propose another family of estimators using the results of B. Prasad (Some improved ratio type estimators of population mean and ratio in finite population sample surveys, Communications in Statistics: Theory and Methods 18, 379-392, 1989). Expressions for the bias and MSE of the proposed family are derived. Besides, considering the minimum cases of these MSE equations, a comparison of the efficiency conditions between the Khoshnevisan and proposed families are obtained. The proposed family of estimators is found to be more efficient than Khoshnevisan's family of estimators under certain conditions. Finally, these theoretical findings are illustrated by a numerical example with original data.
International Journal of Science for Global Sustainability, 2023
In sampling theory, it is a popular trend to use auxiliary information to obtain more efficient estimators for the population parameters to increase the precision of the estimator. Estimators obtained using auxiliary information are supposed to be more efficient than the estimators obtained without using auxiliary information. The ratio, regression, product and difference methods take advantage of the auxiliary information at the estimation stage. Therefore, this study considered a generalized class of log-type estimators of finite population mean based on correlation coefficient as the proposed estimator for estimating the population mean of the study variable. It has been shown that the generalized class of log-type estimators has lesser mean square errors (MSEs) under the optimum values of the characterizing scalar as compared to some of the commonly used related estimators available in the literature. Further, an extension of the proposed generalized class of log-type estimators using multiple auxiliary variables such as coefficient of variation () X C , coefficient of kurtosis () () 2 x , and correlation coefficient () xy . have also base initiated in this dissertation. The expressions for the properties of the proposed family of estimators, that is; Bias and Mean Square Error (MSE), were derived to the first degree of approximation. We also obtained the optimum Mean Square Error (MSEopt.), and theoretical comparisons were made with the related existing estimators in literature. Following theoretical comparisons, it was demonstrated that the proposed family of estimators was more efficient than various related existing estimators compared with, under the obtained conditions.
An improved general class of estimators for finite population mean in simple random sampling
Communications in Statistics - Theory and Methods, 2020
Recently Pal et al. introduced a mean estimator which generalized most of the known mean estimators. We introduce a class of estimators that performs better than Pal et al. estimator. Expressions for bias and MSE for the proposed estimator are derived up to first order of approximation. We use the six datasets for numerical comparison.
EFFICIENT USE OF SUPPLEMENTARY INFORMATION IN FINITE POPULATION SAMPLING
Tracy et al.[8] have introduced a family of estimators using Srivenkataramana and Tracy ([6],[7]) transformation in simple random sampling. In this article, we have proposed a dual to ratio-cum-product estimator in stratified random sampling. The expressions of the mean square error of the proposed estimators are derived. Also, the theoretical findings are supported by a numerical example. Abstract Singh et al. (20009) introduced a family of exponential ratio and product type estimators in stratified random sampling. Under stratified random sampling without replacement scheme, the expressions of bias and mean square error (MSE) of Singh et al. (2009) and some other estimators, up to the first-and second-order approximations are derived. Also, the theoretical findings are supported by a numerical example.
An Unbiased Estimator of Finite Population Mean Using Auxiliary Information
Journal of Statistical Theory and Applications, 2021
In this paper, an unbiased estimator is constructed by using a linear combination of an estimator of study variable and mean per unit estimator of an auxiliary variable under simple random sampling without replacement scheme. The efficiency of the estimator under optimality compared with the mean per unit estimator, an almost unbiased ratio estimator, an unbiased product estimator, and a regression estimator both theoretically and with the numerical illustration.