Asymptotic Optimum Estimator Research Articles

On the Use of Inverse Exponentiation to Improve the Efficiency of Calibration Estimators in Stratified Double Sampling

This study introduces the concept of inverse exponentiation in formulating calibration weights in stratified double sampling and proposes a more improved calibration estimator based on Koyuncu and Kadilar (2014) calibration estimator. The variance of the proposed logarithmic calibration estimator has been derived under large sample approximation. Calibration asymptotic optimum estimator and its approximate variance estimator are derived for the proposed logarithmic calibration estimator. Results of empirical study showed that the proposed logarithmic calibration estimator performs better than the Koyuncu and Kadilar (2014) calibration estimator with appreciable gains in efficiency. Also, simulation study for the comparison of the proposed logarithmic estimator with a Global estimator [Generalized Regression (GREG) estimator ] proved the robustness of the proposed logarithmic calibration estimator and by extension the efficacy of inverse exponentiation in calibration weightings. Analysis and evaluation are presented. International Journal of Statistical Sciences, Vol.24(1), March, 2024, pp 91-102

Modified Classes of Stratified Exponential Ratio Estimators of Population Mean with Equal Optimal Efficiency

This paper introduces new classes of exponential ratio estimators for population mean and derives expressions for their biases and mean square errors (MSEs) under the large sample approximation. Asymptotic optimum estimator and its approximate MSE are derived for each class of estimators. Their properties are studied and some special members of their families are identified. Analytically, the proposed classes of estimators have been shown to have equal optimal efficiency under certain prescribed conditions. It is observed that the proposed classes of estimators fare better than the regression estimator and all the modified existing estimators under review with appreciable efficiency gains.

Efficient class of ratio cum median estimators for estimating the population median.

In estimation theory, the use of auxiliary information significantly improves precision while estimating population parameters. In this paper, an efficient class of ratio cum median estimators of the population median is suggested using simple random sampling without replacement. The expressions for bias and mean square error of the proposed class are derived theoretically. The condition for the asymptotic optimum estimator is obtained with its bias and mean square error expressions. Under certain realistic conditions, the asymptotic optimum estimator is more proficient, based on analytical and numerical comparisons with some existing estimators that are members of the suggested class of estimators. The superiority of the proposed ratio cum median estimators is shown through real data applications. Such a new proposed estimator will be useful in the future for data analysis and making decisions.

Exponential ratio estimator of the median: An alternative to the regression estimator of the median under stratified sampling

This article develops statistical inference about the population median under the stratified sampling method. An exponential class of ratio estimators of the median was suggested using the combination of scalars and known supplementary information on the population median. Mean square error and bias expressions were derived theoretically and also the AOE (asymptotic optimum estimator) conditions were obtained with its mean square error and bias expressions. From both the empirical evidence and analytical approach evaluations of the AOE with other obtainable members of the suggested class of estimators show that the AOE performs better than its competitors in the literature and is also the alternative to the regression estimator of the median under a stratified random sampling scheme.

Ratio-product estimator in stratified double sampling based on coefficient of skewness of the auxiliary variable

In this paper, a ratio-product estimator for estimating the population mean of the study variable based on the population coefficient of skewness of the auxiliary variable is suggested in stratified double sampling. Asymptotic optimum estimator and its approximate bias and variance expressions are derived. Properties of the suggested estimator are studied with some known existing estimators identified as special members of this class of estimators. Analytical and numerical investigations showed that the suggested estimator is more efficient than the conventional regression estimator of mean in stratified double sampling and existing estimators of its class in stratified double sampling. Analysis and evaluation are presented.

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 note on calibration weightings for stratified double sampling with equal probability

ABSTRACTThis study proposes a more efficient calibration estimator for estimating population mean in stratified double sampling using new calibration weights. The variance of the proposed calibration estimator has been derived under large sample approximation. Calibration asymptotic optimum estimator and its approximate variance estimator are derived for the proposed calibration estimator and existing calibration estimators in stratified double sampling. Analytical results showed that the proposed calibration estimator is more efficient than existing members of its class in stratified double sampling. Analysis and evaluation are presented.

A modified ratio-product estimator of population mean using some known parameters of the auxiliary variable

The estimation of population mean is one of the challenging aspects in sampling theory and population study and much effort has been vigorously employed to improve the precision of estimates. In this research work, a modified ratio-product estimator of population mean Y of the study variable Y using median and coefficient of variation of the auxiliary variabl X , in simple random sampling scheme is proposed. The expression of bias and MSE of the proposed estimator have been obtained under large sample approximation, asymptotically optimum estimator (AOE) is identified with its approximate MSE formula. Estimator based on “estimated optimum values” was also investigated. Theoretical and empirical comparison of proposed estimator with some other ratio and product estimators justified the performance of the proposed estimators. A minimum of 20 percent reduction in the MSE were observed from each of the existing estimators considered. It is found that the proposed estimator were uniformly better than all other modified ratio and product estimators and thus most preferred over the existing estimators for the use in practical application. Keywords: Finite population mean, bias, mean square error, auxiliary variable, optimum estimator, study variable

Modified ratio-product estimator of population mean in the presence of median and coefficient of variation of the auxiliary variable in stratified random sampling

For the past decades, the estimation of population mean is one of the challenging aspects in sampling survey techniques and much effort has been employed to improve the precision of estimates. In this research work, we proposed a modified ratio-product estimator of population mean of the variable of interest using median and coefficient of variation of the auxiliary variable in stratified random sampling scheme. The expression of bias and MSE of the proposed estimator have been obtained under large sample approximation, asymptotically optimum estimator (AOE) is identified with its approximate MSE formula. Estimator based on “estimated optimum values” was also investigated. Theoretical and empirical comparison of proposed estimator with some other ratio and product estimator justified the performance of the proposed estimator. There is a minimum of 15 percent reduction in the MSE from each of the existing ratio and product estimators considered. Thus most preferred over the existing estimators for the use in practical application.Keywords: bias, mean square error, auxiliary variable, optimum estimator, stratified random sampling, study variable

Improvement over variance estimation using auxiliary information in sample surveys

ABSTRACTThis paper addresses the problem of estimating the population variance S2y of the study variable y using auxiliary information in sample surveys. We have suggested a class of estimators of the population variance S2y of the study variable y when the population variance S2x of the auxiliary variable x is known. Asymptotic expressions of bias and mean squared error (MSE) of the proposed class of estimators have been obtained. Asymptotic optimum estimators in the proposed class of estimators have also been identified along with its MSE formula. A comparison has been provided. We have further provided the double sampling version of the proposed class of estimators. The properties of the double sampling version have been provided under large sample approximation. In addition, we support the present study with aid of a numerical illustration.

A new family of estimators of the population variance using information on population variance of auxiliary variable in sample surveys

This paper proposes a family of estimators of population variance S2y of the study variable y in the presence of known population variance S2x of the auxiliary variable x. It is identified that in addition to many, the recently proposed classes of estimators due to Sharma and Singh (2014) and Singh and Pal (2016) are members of the proposed family of estimators. Asymptotic expressions of bias and mean squared error (MSE) of the suggested family of estimators have been obtained. Asymptotic optimum estimator (AOE) in the family of estimators is identified. Some subclasses of estimators of the proposed family of estimators have been identified along with their properties. We have also given the theoretical comparisons among the estimators discussed in this paper.

A New Family of Estimators of the Population Variance using Information on Population Variance of Auxiliary Variable in Sample Surveys

Abstract This paper proposes a family of estimators of population variance S 2 y of the study variable y in the presence of known population variance S 2 x of the auxiliary variable x. It is identified that in addition to many, the recently proposed classes of estimators due to Sharma and Singh (2014) and Singh and Pal (2016) are members of the proposed family of estimators. Asymptotic expressions of bias and mean squared error (MSE) of the suggested family of estimators have been obtained. Asymptotic optimum estimator (AOE) in the family of estimators is identified. Some subclasses of estimators of the proposed family of estimators have been identified along with their properties. We have also given the theoretical comparisons among the estimators discussed in this paper.

Generalized ratio-cum-product type exponential estimator in stratified random sampling

ABSTRACTIn this article, we propose a generalized ratio-cum-product type exponential estimator for estimating population mean in stratified random sampling. Asymptotic expression of the bias and mean squared error of the proposed estimator are obtained. Asymptotic optimum estimator in the proposed estimator has been obtained with its mean squared error formula. Conditions under which the proposed estimator is more efficient than usual unbiased estimator, combined ratio and product type estimators, Singh et al. (2008) estimators and Tailor and Chouhan (2014) estimator are obtained. An empirical study has also been carried out.

Generalized Class of Estimators for Population Variance Using Auxiliary Attribute

Singh and Kumar (A family of estimators of population variance using information on auxiliary attribute. Studies in sampling techniques and time series analysis, 2011) and Singh and Malik (Appl Math Comput 235:43–49, 2014) suggested some estimators for estimating the population variance using an auxiliary attribute. This paper suggests a generalized class of estimators based on the adaption of the estimator presented by Koyuncu (Appl Math Comput 218:10900–10905, 2012) for population variance using information on an auxiliary attribute in simple random sampling. The properties of the suggested class of estimators are derived and asymptotic optimum estimator identified with its properties. The large numbers of known estimators are member of the suggested generalized class and it has been shown that proposed generalized class of estimators are more efficient than usual unbiased estimator, ratio, exponential ratio and regression estimator, estimators due to Singh and Malik (Appl Math Comput 235:43–49, 2014) and Singh and Kumar (A family of estimators of population variance using information on auxiliary attribute. Studies in sampling techniques and time series analysis, 2011) using information on auxiliary attribute. In addition, theoretical results are supported by an empirical study and findings are encouraging and support the soundness of present study.

A modified class of ratio estimators for population mean

ABSTRACTA modified class of ratio estimators for population mean of the study variable (ϒ) under the simple random sampling without replacement scheme is proposed using a combination of scalars and known population mean of the auxiliary variable (X). The expressions for the bias and mean square error (MSE) were obtained and the condition for the asymptotic optimum estimator (AOE) with its bias and mean square error expressions were also obtained. Analytical and numerical comparisons of the AOE with other existing members of the proposed class of estimators show that the AOE is more efficient under certain realistic conditions.

A generalized ratio-cum-product estimator for estimating the finite population mean in survey sampling

ABSTRACTThis paper suggested an alternative ratio-cum-product type class of estimators of population mean using exponentiation method in simple random sampling. Approximate bias and mean squared error formulae of the suggested class of estimators have been obtained up to the first order of approximation. Asymptotic optimum estimator in the suggested class of estimators has been obtained with its mean squared error formula. Regions of preferences have been obtained under which the suggested class of estimators has been better than the usual unbiased, ratio and product estimators and the estimators according to Singh and Agnihotri (2008). Some examples are cited with numerical study.

Generalized Class Of Estimators For Population Median Using Auxiliary Information

This article suggests a generalized class of estimators for population median of the study variable in simple random sampling using information on an auxiliary variable. Asymptotic expressions of bias and mean square error of the proposed class of estimators have been obtained. Asymptotic optimum estimator has been investigated along with its approximate mean square error. It has been shown that proposed generalized class of estimators are more efficient than estimators considered by [26] , [5],[6], [22], [1] , [19] and other estimators . In addition theoretical findings are supported by an empirical study based on two populations to show the superiority of the constructed estimators over others. 2000 AMS Classification: 62D05.

Improved Ratio and Product Exponential type Estimators for Finite Population Mean in Stratified Random Sampling

This article addresses the problem of the estimation of the population mean of the study variable y using auxiliary variable x in stratified random sampling. Classes of ratio and product exponential type estimators are proposed. The biases and mean squared errors of the suggested estimators are obtained upto the first order of approximation. Conditions are obtained under which the proposed estimators are better than usual unbiased estimator, conventional combined ratio and product estimators and Singh et al. (2008) estimators. Asymptotic optimum estimators (AOEs) in the proposed classes of estimators are identified alongwith their mean squared errors formulae. Estimators based on estimated optimum values are obtained with their mean squared errors expressions. An empirical study has been carried out to examine the merits of the suggested estimators over others.

Some Classes of Estimators for the Population Median Using Auxiliary Information

This article considers some classes of estimators of the population median of the study variable using information on an auxiliary variable with their properties under large sample approximation. Asymptotic optimum estimator (AOE) in each class of estimators has been investigated along with the approximate mean square error formulae. It has been shown that the proposed classes of estimators are better than these considered by Gross (1980), Kuk and Mak (1989), Singh et al. (2003a), and Al and Cingi (2009). An empirical study is carried out to judge the merits of the suggested class of estimators over other existing estimators.

Efficient classes of estimators in stratified random sampling

This article suggests two generalized classes of estimators of population mean using auxiliary information in stratified random sampling. The properties of the suggested classes are derived and asymptotic optimum estimator in each class is identified with its properties. The large numbers of known estimators are members of the suggested classes such as usual unbiased estimator, usual combined ratio estimator (Hansen et al., Am Stat Assoc 41:173–189, 1946), usual combined product estimator (Kaur, Biom J 27(1):101–105, 1985), and estimators /classes of estimators due to Kaur (Biom J 26(7):749–753, 1984, Biom J 27(1):101–105, 1985), Diana (Statistica 53(1):59–66, 1993), Kadilar and Cingi (Biom J 45(2):218–225, 2003, Commun Stat Theory Methods 34(3):597–602, 2005), Shabbir and Gupta (Am J Math Manag Sci 25(3–4):293–311, 2005), Singh and Vishwakarma (Metodologia de Encuestas, Monografico: Incidencias en el trabjo de Campo 7(1):32–40, 2006a, Stat Trans 7(6):1311–1325, 2006b), Singh et al. (Stat Pap 49(1):37–58, 2008, SORT 34(2):157–180, 2010), Tailor (Data Sci Jour 8:182–189, 2009), Koyuncu and Kadilar (J Stat Plan Inference 139(8):2552–2558, 2009, Pak J Stat 26(2):427–443, 2010b) and Tailor et al. (Commun Korea Stat Soc 18(1):111–118, 2011). The theoretical and empirical studies are carried out and findings are encouraging and support the soundness of the present study.