Housila P. Singh

Use of Transformed Auxiliary Variable in Estimating the Finite Population Mean

For estimating the finite population mean Y of the study character y, an estimator using a transformed auxiliary variable has been defined. The bias and mean-squared error (MSE) of the proposed estimator have been obtained. The regions of preference have been obtained under which it is better than usual unbiased estimator y, the ratio estimator y R = yX/x, SISODIA and DWIVEDI (1981) estimator y s = y(X + C x )/(x + C x ) and SINGH and KAKRAN (1993) estimator y k = y[X + β 2 (x)]/x + β 2 (x)]. An empirical study has been carried out to demonstrate the superiority of the suggested estimator over the others.

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.

Successive Sampling Using Auxiliary Information on Both the Occasions

In successive sampling with partial replacement, an estimator is proposed for the population mean on the second of two successive occasions utilising information available on both the occasions on an auxiliary variate with an unknown population mean. It is shown that the proposed estimator is more efficient than the sample mean and the estimators considered by Sen (1971). An empirical study is also included.

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.

A Stratified Unknown Repeated Trials in Randomized Response Sampling

This paper proposes an alternative stratified randomized response model based on the model of Singh and Joarder (1997). It is shown numerically that the proposed stratified randomized response model is more efficient than Hong et al. (1994) (under proportional allocation ) and Kim and Warde (2004) (under optimum allocation).

Unbiased estimators of finite population variance using auxiliary information in sample surveys

We present some unbiased estimators of the population variance in a finite population sample survey using the knowledge of population variance of an auxiliary character.Exact variance expressions for the proposed estimators are obtained and compared with usual unbiased estimator and the ratio estimator envisaged by Isaki (1983). Generalization of the proposed estimator is also suggested.

Double Sampling Ratio-product Estimator of a Finite Population Mean in Sample Surveys

Abstract It is well known that two-phase (or double) sampling is of significant use in practice when the population parameter(s) (say, population mean X¯) of the auxiliary variate x is not known. Keeping this in view, we have suggested a class of ratio-product estimators in two-phase sampling with its properties. The asymptotically optimum estimators (AOEs) in the class are identified in two different cases with their variances. Conditions for the proposed estimator to be more efficient than the two-phase sampling ratio, product and mean per unit estimator are investigated. Comparison with single phase sampling is also discussed. An empirical study is carried out to demonstrate the efficiency of the suggested estimator over conventional estimators.

Improved Estimation of Finite-Population Mean Using Sub-Sampling to Deal with Non Response in Two-Phase Sampling Scheme

This article proposes some alternative estimators for estimating the population mean of a study variable y using information on an auxiliary variable x in the presence of non response under two-phase sampling. The properties of the suggested estimators are given under a large-sample approximation, and the conditions are obtained in which the suggested estimators are better than the conventional unbiased estimators, usual two-phase sampling ratio, and product estimators. In addition, survey cost aspects are discussed under a linear cost function. A real agricultural population is used to present the application of the proposed estimators.

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 alternative to the ratio-cum-product estimator in sample surveys

Abstract In this paper, using a transformation (Srivenkataramana and Tracy, Ann. Inst. Statist. Math. 32A (1980), 111–120; Austral. J. Statist. 23 (1981), 95–100), an alternative to the usual ratio-cum-product estimator, considered by Singh (Metrika 12 (1967), 34–42), is proposed. Exact expressions for bias and mean square error of the proposed estimator are derived. Under a simple random sampling without replacement (SRSWOR) scheme, an exactly unbiased estimator is obtained with its approximate variance formula. The conditions for the proposed unbiased estimator to be more efficient than the conventional unbiased estimator y , usual ratio ( y R ) and product ( y P ) estimators, Singth (Metrika 12 (1967), 34–42) and Srivenkataramana and Tracy (Ann. Inst. Statist. Math. 32A (1980), 111–120) estimators are derived. An empirical study is carried out to demonstrate the efficiency of the proposed estimator over the other estimators.