Asymptotic Optimum Estimator Research Articles

Almost unbiased ratio and product type exponential estimators

This paper considers the problem of estimating the population mean Y of the study variate y using information on auxiliary variate x. We have suggested a generalized version of Bahl and Tuteja (1991) estimator and its properties are studied. It is found that asymptotic optimum estimator (AOE) in the proposed generalized version of Bahl and Tuteja (1991) estimator is biased. In some applications, biasedness of an estimator is disadvantageous. So applying the procedure of Singh and Singh (1993) we derived an almost unbiased version of AOE. A numerical illustration is given in the support of the present study.

Efficient Ratio and Product Estimators in Stratified Random Sampling

This paper suggests an efficient class of ratio and product estimators for estimating the population mean in stratified random sampling using auxiliary information. It is interesting to mention that, in addition to many, Koyuncu and Kadilar (2009), Kadilar and Cingi (2003, 2005), and Singh and Vishwakarma (2007) estimators are identified as members of the proposed class of estimators. The expressions of bias and mean square error (MSE) of the proposed estimators are derived under large sample approximation in general form. Asymptotically optimum estimator (AOE) in the class is identified alongwith its MSE formula. It has been shown that the proposed class of estimators is more efficient than combined regression estimator and Koyuncu and Kadilar (2009) estimator. Moreover, theoretical findings are supported through a numerical example.

An Efficient Class of Estimators for the Population Mean Using Auxiliary Information

This article addresses the problem of estimating the population mean in the presence of auxiliary information. A class of estimators for population mean is defined. Asymptotic expressions of the bias and mean squared error of the proposed class of estimators were obtained. Asymptotic optimum estimator (AOE) in the proposed class of estimators was identified along with its mean squared error formula. It has been shown that the proposed class of estimators is more efficient than the usual regression estimator and Khoshnevisan et al. (2007), Singh et al. (2007), and Koyuncu and Kadilar (2009a) classes of estimators.

AN IMPROVEMENT OVER REGRESSION METHOD OF ESTIMATION

This paper suggested a class of estimators for the population mean of the study variable using information on an auxiliary variable with its properties under large sample approximation. The asymptotic optimum estimator in the proposed class has been identified with its properties. In addition, some existing estimators have been founded members of proposed class. It has been identified theoretically that the proposed class of estimators is better than the some traditional methods of estimation. An empirical study is carried out to judge the merits of proposed class over other competitors by using two natural population data sets.

Families of Estimators of Finite Population Variance using a Random Non-Response in Survey Sampling

In this paper, a family of estimators for the finite population variance investigated by Srivastava and Jhajj (1980) is studied under two different situations of random non-response considered by Tracy and Osahan (1994). Asymptotic expressions for the biases and mean squared errors of members of the proposed family are obtained; in addition, an asymptotic optimum estimator(AOE) is also identified. Estimators suggested by Singh and Joarder (1998) are shown to be members of the proposed family. A correction to the Singh and Joarder (1998) results is also presented.

An Alternative Estimator for Estimating the Finite Population Mean Using Auxiliary Information in Sample Surveys

This paper suggests a class of estimators for estimating the finite population mean of the study variable using known population mean of the auxiliary variable . Asymptotic expressions of bias and variance of the suggested class of estimators have been obtained. Asymptotic optimum estimator (AOE) in the class is identified along with its variance formula. It has been shown that the proposed class of estimators is more efficient than usual unbiased, usual ratio, usual product, Bahl and Tuteja (1991), and Kadilar and Cingi (2003) estimators under some realistic conditions. An empirical study is carried out to judge the merits of suggested estimator over other competitors practically.

A new procedure for variance estimation in simple random sampling using auxiliary information

In this article we have envisaged an efficient generalized class of estimators for finite population variance of the study variable in simple random sampling using information on an auxiliary variable. Asymptotic expressions of the bias and mean square error of the proposed class of estimators have been obtained. Asymptotic optimum estimator in the proposed class of estimators has been identified with its mean square error formula. We have shown that the proposed class of estimators is more efficient than the usual unbiased, difference, Das and Tripathi (Sankhya C 40:139–148, 1978), Isaki (J. Am. Stat. Assoc. 78:117–123, 1983), Singh et al. (Curr. Sci. 57:1331–1334, 1988), Upadhyaya and Singh (Vikram Math. J. 19:14–17, 1999b), Kadilar and Cingi (Appl. Math. Comput. 173:2, 1047–1059, 2006a) and other estimators/classes of estimators. In the support of the theoretically results we have given an empirical study.

Improved estimation of population mean in simple random sampling using information on auxiliary attribute

This paper addresses the problem of estimating the population mean with known population proportion of an auxiliary variable. A class of estimators is defined which includes the estimators recently proposed by Shabbir and Gupta (2007) [10] and Abd-Elfattah et al. (2010) [1]. The usual unbiased estimator and Naik and Gupta (1996) [15] estimator are also the member of the proposed class of the estimators. The bias and mean square error (MSE) expressions of the proposed class are obtained up to first order of approximation. Asymptotically optimum estimator (AOE) in the class of estimators is identified alongwith its mean square error formula. The correct MSE and minimum MSE expressions of Shabbir and Gupta (2007) [10] estimator are also given. It has been shown that the proposed class of estimators is more efficient than the usual unbiased estimator, usual linear regression estimator and estimators/classes of estimators due to Naik and Gupta (1996) [15], Jhajj et al. (2008) [9], Shabbir and Gupta (2007) [10] estimator, Singh et al. (2008) [13] and Abd-Elfattah et al. (2010) [1]. The double sampling version of the proposed class of estimators is proposed alongwith its properties. Numerical illustrations are given in support of the present study.

A general procedure for estimating the mean using double sampling for stratification and multi-auxiliary information

This paper defines a general procedure for estimating the population mean of the study variate based on double sampling for stratification in presence of multi-auxiliary information. Classes of combined and separate estimators have been suggested and their properties are studied under large sample approximation. A class of unstratified double sampling estimators is also proposed with its properties. Asymptotic optimum estimators in the classes are identified with their approximate variance formulae. Further the proposed classes of estimators are compared with the corresponding class of estimators based on un-stratified double sampling. All findings are encouraging and support the soundness of the proposed procedure for mean estimation.

A generalized method of estimation of a population parameter in two-phase and successive sampling

The paper considers a problem of estimating a finite population parameter T (α, β, γ) in two-phase and successive sampling. Asymptotic optimum estimator (AOE) in a class is identified with its approximate variance formula. Several estimators of different parameters are identified as particular members of the class. In particular, we have focused on estimating the population coefficient of variation. The expressions for bias and variance are derived and compared theoretically.

Efficient Use of Auxiliary Variables in Estimating Finite Population Variance in Two-Phase Sampling

This paper presents some chain ratio-type estimators for estimating finite population variance using two auxiliary variables in two phase sampling set up. The expressions for biases and mean squared errors of the suggested c1asses of estimators are given. Asymptotic optimum estimators(AOE's) in each class are identified with their approximate mean squared error formulae. The theoretical and empirical properties of the suggested classes of estimators are investigated. In the simulation study, we took a real dataset related to pulmonary disease available on the CD with the book by Rosner, (2005).

A General Family of Estimators of Finite Population Ratio, Product and Mean Using Two Phase Sampling Scheme in the Presence of Non-Response

This paper deals with the problem of estimating the population ratio, product and mean using auxiliary information in two-phase sampling in presence of non-response. Three classes of estimators are proposed along with their properties. Asymptotic optimum estimators (AOEs) have been investigated with their approximate mean squared error formulae. Estimators based on estimated optimum values have also been given. It has been shown that to the first degree of approximation the mean squared errors of the estimators based on estimated optimum values have the mean squared errors equal to the mean squared errors of asymptotic optimum estimators (AOEs). An empirical study is carried to show the performance of the various estimators relative to the conventional estimator.

A Family of Estimators of Population Mean Using Auxiliary Information in Stratified Sampling

This article suggests a family of estimators of population mean using auxiliary information in stratified sampling. The bias and mean-squared error of the suggested family of estimators are derived under large sample approximation. Asymptotic optimum estimator (AOE) in the class of estimators is investigated with its mean-squared error formula. It is identified that the usual unbiased estimator , traditional combined ratio estimator , traditional combined regression estimator , Kadilar and Cingi (2005) estimator , and Shabbir and Gupta (2006) estimator are particular members of a suggested family of estimators. The new expressions of bias and a mean-square error of Kadilar and Cingi (2005) estimator and a new expression of a mean-square error of Shabbir and Gupta (2006) estimator have been derived. Both theoretical and empirical findings are encouraging and support the soundness of the present study.

A Family of Estimators of a Density Using Concomitant Variable and Additional Data

In this paper we have suggested a family of estimators of a density f( y) of a random variable Y based upon a set of observations taken from a bivariate joint density β( x, y) of Y and a suitably chosen concomitant random variable X so that f( y) = ∫ β( x, y) dx. It is shown that the estimator envisaged by Ahmad and Singh (1989) is a particular member of the proposed family. Asymptotic expressions for bias and variance of the proposed family are obtained. Asymptotically optimum estimator (AOE) in the class is also identified.

An Improved Class of Estimators for Finite Population Mean in Sample Surveys

This paper proposes a class of estimators for estimating the finite population mean Y of a study variate y using information on two auxiliary variates, one of which is positively and the other negatively correlated with the study variate y. An asymptotically optimum estimator (AOE) in the class is identified with its bias and mean square error formulae. It is observed that the proposed AOE is more efficient than SRIVASTAVA (1965), SRIVASTAVA (1974), PRASAD (1989) and GANDGE, VARGHESE, and PRABHU-AJGAONKAR (1993) estimators.

Estimation of ratio and product of two finite population means in two-phase sampling

A class of estimators for estimating ratio and product of two finite population means in two-phase sampling is proposed. Asymptotic expressions for bias and mean squared error (MSE) are obtained. Asymptotic optimum estimators (AOEs) are also identified. An empirical study is carried out to illustrate the performances of the constructed estimator over usual estimator.