Javid Shabbir

On improvement in estimating the population mean in simple random sampling

Abstract Kadilar and Cingi [Ratio estimators in simple random sampling, Appl. Math. Comput. 151 (3) (2004), pp. 893–902] introduced some ratio-type estimators of finite population mean under simple random sampling. Recently, Kadilar and Cingi [New ratio estimators using correlation coefficient, Interstat 4 (2006), pp. 1–11] have suggested another form of ratio-type estimators by modifying the estimator developed by Singh and Tailor [Use of known correlation coefficient in estimating the finite population mean, Stat. Transit. 6 (2003), pp. 655–560]. Kadilar and Cingi [Improvement in estimating the population mean in simple random sampling, Appl. Math. Lett. 19 (1) (2006), pp. 75–79] have suggested yet another class of ratio-type estimators by taking a weighted average of the two known classes of estimators referenced above. In this article, we propose an alternative form of ratio-type estimators which are better than the competing ratio, regression, and other ratio-type estimators considered here. The results are also supported by the analysis of three real data sets that were considered by Kadilar and Cingi.

On estimation of finite population variance

Abstract Following Searls (1964), we propose an estimator for estimating the finite population variance. This estimator is the combination of Singh et al. (1973), and Prasad and Singh (1992) estimators and has an improvement over Singh et al. (1973), Prasad and Singh (1992), and several other estimators under certain conditions. Validity of proposed estimator is examined by using seven numerical examples.

A New Estimator of Population Mean in Stratified Sampling

Kadilar and Cingi (2005) have suggested a new ratio estimator in stratified sampling. The efficiency of this estimator is compared with the traditional combined ratio estimator on the basis of mean square error (MSE). We propose another estimator by utilizing a simple transformation introduced by Bedi (1996). The proposed estimator is found to be more efficient than the traditional combined ratio estimator as well as the Kadilar and Cingi (2005) ratio estimator.

Improved Ratio Estimators in Stratified Sampling

SYNOPTIC ABSTRACT KADILAR and CINGI (2003) proposed some classes of combined ratio estimators for estimating the population mean by using transformations introduced by SISODIA and DWIVEDI (1981), SINGH and KAKRAN (1993) and UPADHYAYA and SINGH (1999). In this paper, we introduce a class of combined ratio-type estimators, which is more efficient than the usual combined ratio estimator; a class of estimators introduced by KADILAR and CINGI (2003), and is as efficient as the combined linear regression estimator.

On Improvement in Variance Estimation Using Auxiliary Information

Kadilar and Cingi (2006) have introduced an estimator for the population variance using an auxiliary variable in simple random sampling. We propose a new ratio-type exponential estimator for population variance which is always more efficient than usual ratio and regression estimators suggested by Isaki (1983) and by Kadilar and Cingi (2006). Efficiency comparison is carried out both mathematically and numerically.

On Estimating Finite Population Mean in Simple and Stratified Random Sampling

In this article, we propose an exponential ratio type estimator for estimating the finite population mean in simple and stratified random sampling. The properties of the proposed estimator are obtained and comparison is made with some of the existing estimators. The proposed estimator is found to perform better than the usual mean, ratio, exponential ratio, traditional regression and Pandy (1980) estimators in simple and stratified random sampling. We use six data sets for simple random sampling case and two data sets for stratified random sampling case to compare the performances of all of the estimators considered here.

Estimation of the Mean of a Sensitive Variable in the Presence of Auxiliary Information

Sousa et al. (2010) introduced a ratio estimator for the mean of a sensitive variable and showed that this estimator performs better than the ordinary mean estimator based on a randomized response technique (RRT). In this article, we introduce a regression estimator that performs better than the ratio estimator even for modest correlation between the primary and the auxiliary variables. The underlying assumption is that the primary variable is sensitive in nature but a non sensitive auxiliary variable exists that is positively correlated with the primary variable. Expressions for the Bias and MSE (Mean Square Error) are derived based on the first order of approximation. It is shown that the proposed regression estimator performs better than the ratio estimator and the ordinary RRT mean estimator (that does not utilize the auxiliary information). We also consider a generalized regression-cum-ratio estimator that has even smaller MSE. An extensive simulation study is presented to evaluate the performances of the proposed estimators in relation to other estimators in the study. The procedure is also applied to some financial data: purchase orders (a sensitive variable) and gross turnover (a non sensitive variable) in 2009 for a population of 5,336 companies in Portugal from a survey on Information and Communication Technologies (ICT) usage.

Ratio Estimation of the Mean of a Sensitive Variable in the Presence of Auxiliary Information

We propose a ratio estimator for the mean of sensitive variable utilizing information from a non-sensitive auxiliary variable. Expressions for the Bias and MSE of the proposed estimator (correct up to first and second order approximations) are derived. We show that the proposed estimator does better than the ordinary RRT mean estimator that does not utilize the auxiliary information. We also show that there is hardly any difference in the first order and second order approximations for MSE even for small sample sizes. We also generalize the proposed estimator to the case of transformed ratio estimators but these transformations do not result in any significant reduction in MSE. An extensive simulation study is presented to evaluate the performance of the proposed estimator. The procedure is also applied to some financial data (purchase orders (sensitive variable) and gross turn-over (non-sensitive variable)) in 2009 for 5090 companies in Portugal from a survey on Information and Communication Technologies (ICT) usage.

A Three-Stage Optional Randomized Response Model

In Gupta et al. (2010; 2011), it was observed that introduction of a truth element in an optional randomized response model can improve the efficiency of the mean estimator. However, a large value of the truth parameter (T) may be needed if the underlying question is highly sensitive. This can jeopardize respondent cooperation. In what we call a “three-stage optional randomized response model,” a known proportion (T) of the respondents is asked to tell the truth, another known proportion (F) of the respondents is asked to provide a scrambled response, and the remaining respondents are instructed to provide a response following the usual optional randomized response strategy where a respondent provides a truthful response (or a scrambled response) depending on whether he/she considers the question nonsensitive (or sensitive). This is done anonymously based on color-coded cards that the researcher cannot see. In this article we show that a three-stage model may turn out to be more efficient than the corresponding two-stage model, and with a smaller value of T. Greater respondent cooperation will be an added advantage of the three-stage model.

Generalized Scrambling in Quantitative Optional Randomized Response Models

Huang (2010) proposed an optional randomized response model using a linear combination scrambling which is a generalization of the multiplicative scrambling of Eichhorn and Hayre (1983) and the additive scrambling of Gupta et al. (2006, 2010). In this article, we discuss two main issues. (1) Can the Huang (2010) model be improved further by using a two-stage approach?; (2) Does the linear combination scrambling provide any benefit over the additive scrambling of Gupta et al. (2010)? We will note that the answer to the first question is “yes” but the answer to the second question is “no.”