Ramkrishna S. Solanki

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

Abstract 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.

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 𝑌 of the study variable 𝑦 using known population mean 𝑋 of the auxiliary variable 𝑥. 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.

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

This article addresses the problem of estimating the population mean in systematic sampling using information on an auxiliary variable. A class of estimators for the population mean is defined with its properties under large sample approximation. It has been shown that the proposed class of estimators is better than the usual unbiased estimator, Swain (1964) estimator, Shukla (1971) estimator, and usual regression estimator. The results have been illustrated through an empirical study.

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 improved class of estimators for the population variance

Startingfrom the Singh et al. (28) (Current Science 57: 1331-1334) difference estimator, we define a class of estimators for the unknown variance of a survey variable on the line of Diana et al. (7) (Stat Methods Appl DOI 10.1007/s10260-010-0156- 6) when auxiliary variable is available. The bias and mean square error of the estimators belonging to the class of estimators are derived and the expressions for the optimum parameters minimizing the asymptotic mean square error are given in closed form. A simple condition allowing us to improve the usual difference estimator due to Das and Tripathi (6) (Sankhya C 40: 139-148) is derived. Finally, in order to judge the merits of some estimators with the usual difference one, an empirical study is carried out.

Improved Estimation of Finite Population Variance Using Auxiliary Information

This article addresses the problem of estimating of finite population variance using auxiliary information in simple random sampling. A ratio-cum-difference type class of estimators for population variance has been suggested with its properties under large sample approximation. It has been shown that the suggested class of estimators is more efficient than usual unbiased, difference, Das and Tripathi (1978), Isaki (1983), Singh et al. (1988), Kadilar and Cingi (2006), and other estimators/classes of estimators. In addition, we support this theoretical result with the aid of a empirical study.

Improved ratio-type estimators of finite population variance using quartiles

In this paper we have proposed some ratio-type estimators of finite population variance using known values of parameters related to an auxiliary variable such as quartiles with their properties in simple random sampling. The suggested estimators have been compared with the usual unbiased and ratio estimators and the estimators due to [2], [12, 13, 14] and [3]. An empirical study is also carried out to judge the merits of the proposed estimator over other existing estimators of population variance using natural data set. 2000 AMS Classification: 62D05

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.

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.

Estimation of Bowley's Coefficient of Skewness in the Presence of Auxiliary Information

In this paper, we suggest regression-type estimators for estimating the Bowleys coefficient of skewness using auxiliary information. To the first degree of approximation, the bias and mean-squared error expressions of the regression-type estimators are obtained, and the regions under which these estimators are more efficient than the conventional estimator are also determined. Further, a general class of estimators of the Bowleys coefficient of skewness is defined along with its properties. A class of estimators based on estimated optimum values is also defined. It is shown to the first degree of approximations that the variance of the class of estimators based on estimated optimum values is the same as that of the minimum variance of the proposed class of estimators. A simulation study is carried out to demonstrate the performance of the proposed difference estimator over the usual estimator.