Calibration Approach-based Product Estimator of Finite Population Total with Subsampling of Nonrespondents under Single and Two-phase Sampling

Hansen and Hurwitz (1946) technique–based estimator of population total is proposed using the calibration approach under the assumption that the auxiliary variable is negatively correlated with the study variable. The variance estimation is also considered. The two-phase sampling case is also explored. The theoretical results are demonstrated through empirical studies using both generated and real population data. The proposed estimator of population total outperforms the existing estimators in terms of the criteria of relative bias and relative root mean square error.     

Calibrated estimators in two-stage sampling

We consider the problem of the estimation of the population mean of a study variable by assuming that the population means of an auxiliary variable are known at both stages of sample selection. The design weights at the first and second stages of sample selection are calibrated by optimizing the chi-squared type distance between the design weights and the new weights at both the first and second stages of sample selection. The regression type estimator in two-stage sampling is shown to be a special case. An application of the proposed estimators using a real data set is discussed.     

Estimation of population mean based on dual use of auxiliary information in non response

Whenever there is auxiliary information available in any form, the researchers want to utilize it in the method of estimation to obtain the most efficient estimator. When there exists enough amount of correlation between the study and the auxiliary variables, and parallel to these associations, the ranks of the auxiliary variables are also correlated with the study variable, which can be used a valuable device for enhancing the precision of an estimator accordingly. This article addresses the problem of estimating the finite population mean that utilizes the complementary information in the presence of (i) the auxiliary variable and (ii) the ranks of the auxiliary variable for non response. We suggest an improved estimator for estimating the finite population mean using the auxiliary information in the presence of non response. Expressions for bias and mean squared error of considered estimators are derived up to the first order of approximation. The performance of estimators is compared theoretically and numerically. A numerical study is carried out to evaluate the performances of estimators. It is observed that the proposed estimator is more efficient than the usual sample mean and the regression estimators, and some other families of ratio and exponential type of estimators.     

Improved estimation of population mean using known median of auxiliary variable

In this article, we consider the problem of estimation of population mean using the known median of auxiliary variable. We proposed an estimator and its efficiency is studied analytically as well as empirically for different conditions. The proposed estimator is found to be more efficient than traditional estimators such as sample mean and linear regression estimator.     

Classes of estimators for population mean using auxiliary variable in stratified population in the presence of non response

In this article, we have proposed six classes of estimators for population mean using auxiliary variable in stratified population with known population mean in the presence of non response on the study variable. The properties of the proposed class of estimators have been studied for fixed sample size. An empirical study has been given in the support of the proposed classes of the estimator.     

A Class of Estimators of Population Variance Using Auxiliary Information in Sample Surveys

This article advocates the problem of estimating the population variance of the study variable using information on certain known parameters of an auxiliary variable. A class of estimators for population variance using information on an auxiliary variable has been defined. In addition to many estimators, usual unbiased estimator, Isaki's (1983), Upadhyaya and Singh's (1999), and Kadilar and Cingi's (2006) estimators are shown as members of the proposed class of estimators. Asymptotic expressions for bias and mean square error of the proposed class of estimators have been obtained. An empirical study has been carried out to judge the performance of the various estimators of population variance generated from the proposed class of estimators over usual unbiased estimator, Isaki's (1983), Upadhyaya and Singh's (1999) and Kadilar and Cingi's (2006) estimators.     

Estimation of mean in presence of non-response using two phase sampling scheme

This paper considers the problem of estimating the population mean using information on an auxiliary variable in presence of non-response. Some modified ratio, product and regression estimators in double sampling have been suggested and their properties are studied. It is shown that to the first degree of approximation, estimators based on estimated optimum values have the same variance as that of the optimum estimators. An empirical study is carried to judge the merits of the suggested estimators over conventional unbiased estimator and other known estimators. Both theoretical and empirical study results present the soundness and usefulness of the suggested estimators in practice.     

A Class of Estimators Using Auxiliary Information for Estimating Finite Population Variance in Presence of Measurement Errors

This article addresses the problem of estimating the population variance using auxiliary information in the presence of measurement errors. When the measurement error variance associated with study variable is known, a class of estimators of the population variance using auxiliary information has been proposed. We obtain the bias and mean squared errors of the suggested class of estimators upto the terms of order n ^?1, and also optimum estimators in asymptotic sense of the class with approximate mean squared error formula.     

A simulation study: estimation of population mean using two auxiliary variables in stratified random sampling

ABSTRACT

This paper deals with the problem of estimating the finite population mean in stratified random sampling by using two auxiliary variables. This paper proposed a ratio-cum-product exponential type estimator of population mean under different situations: (i) when there is presence of non-response and measurement errors on the study as well as auxiliary variables; (ii) when there is non-response on the study and auxiliary variables but with no measurement error; (iii) when there is complete response on study variable but there is presence of non-response and measurement error on the auxiliary variables and (iv) when there are complete response and measurement error on study as well as auxiliary variables. The expressions of the bias and mean square error of the proposed estimator have been obtained up to the first degree of approximation. The proposed estimator has been compared with usual unbiased estimator, ratio estimator and other existing estimators and the conditions obtained to show the efficacy of the proposed estimator over other considered estimators. Simulation study is carried out to support the theoretical findings.     

Hansen and Hurwitz estimator with scrambled response on the second call

In this paper we propose a modified version of the estimator of Hansen and Hurwitz [12] in the case of quantitative sensitive variable and consider a randomization mechanism on the second call that provides privacy protection to the respondents to get truthful information. We use variance of the modified estimator as a tool to measure privacy protection and it is observed that the higher is the variance, the lower is the efficiency but the higher is the privacy protection. To overcome this efficiency loss, we consider a linear regression estimator using known non-sensitive auxiliary information. With consideration of four scrambled models, we try to make a trade-off between efficiency and privacy protection. To show this compromise, analytical and numerical comparisons are obtained.     

Partially Calibrated Poststratified Weights for Handling Unit Non Response

We consider a non response-adjusted poststratified estimation when there exists a set of clear response homogeneity groups but the population distribution of that set is unknown, which is common in practice. We propose a partially calibrated poststratified estimator that is asymptotically unbiased and satisfies a calibration equation for the auxiliary variables of which the joint population distribution is known. We also provide a variance estimator of the proposed poststratified estimator. In a small simulation study, the proposed estimator performed better than or comparable to commonly used estimators.     

Estimation of population mean in presence of random non response in two-stage cluster sampling

The present investigation addresses the problem of estimating a finite population mean in two-phase cluster sampling in presence of random non response situations. Utilizing information on an auxiliary variable, regression type estimators has been proposed. Effective imputation techniques have been suggested to deal with the random non response situations. The properties of the proposed estimation strategies have been studied for different cases of random non response situations in practical surveys. The superiority of the suggested methodology over the natural sample mean estimator of population mean has been established through empirical studies carried over the data sets of natural population and artificially generated population.     

Calibration approach for estimating population total with subsampling of non respondents under single- and two-phase sampling

ABSTRACT

Using the calibration approach, the Hansen and Hurwitz (1946 Hansen, M.H., Hurwitz, W.N. (1946). The problem of non response in sample surveys. J. Am. Stat. Assoc. 46:147–190.[Taylor & Francis Online] , [Google Scholar]) technique-based estimator is developed for the situation where the information on auxiliary variable is assumed known for the entire population units. The double-sampling case has also been dealt with. Expressions for the estimator of population total, its variance, and variance estimator are developed. The theoretical results are illustrated with the help of simulation studies. Simulation results show that the proposed calibration approach-based estimator outperforms the Hansen and Hurwitz estimator.     

New calibration estimator in stratified sampling

This paper develops the theory of calibration estimation and proposes calibration approach alternative to existing calibration estimators for estimating population mean of the study variable using auxiliary variable in stratified sampling. The theory of new calibration estimation is given and optimum weights are derived. A simulation study is carried out to performance of the proposed calibration estimator with other existing calibration estimators. The results reveal that the proposed calibration estimators are more efficient than Tracy et al., Singh et al., Singh calibration estimators of the population mean.     

A Generalized Class of Ratio Type Exponential Estimators of Population Mean Under Linear Transformation of Auxiliary Variable

Recently, Shabbir and Gupta [Shabbir, J. and Gupta, S. (2011). On estimating finite population mean in simple and stratified random sampling. Communications in Statistics-Theory and Methods, 40(2), 199–212] defined a class of ratio type exponential estimators of population mean under a very specific linear transformation of auxiliary variable. In the present article, we propose a generalized class of ratio type exponential estimators of population mean in simple random sampling under a very general linear transformation of auxiliary variable. Shabbir and Gupta's [Shabbir, J. and Gupta, S. (2011). On estimating finite population mean in simple and stratified random sampling. Communications in Statistics-Theory and Methods, 40(2), 199–212] class of estimators is a particular member of our proposed class of estimators. It has been found that the optimal estimator of our proposed generalized class of estimators is always more efficient than almost all the existing estimators defined under the same situations. Moreover, in comparison to a few existing estimators, our proposed estimator becomes more efficient under some simple conditions. Theoretical results obtained in the article have been verified by taking a numerical illustration. Finally, a simulation study has been carried out to see the relative performance of our proposed estimator with respect to some existing estimators which are less efficient under certain conditions as compared to the proposed estimator.     

Estimation of coefficient of dispersion using auxiliary information

In this note, we consider the problem of estimation of coefficient of dispersion of a study variable by making use of known value of the coefficient of dispersion of an auxiliary variable. We propose ratio and regression-type estimators. We derive expressions of bias and variance of the proposed estimators to the first order of approximation. The relative efficiencies of the ratio and regression-type estimators with respect to the naïve estimator are investigated through a simulation study.     

A dual problem of calibration of design weights

In this note, a dual problem to the calibration of design weights of the Deville and Särndal [Calibration estimators in survey sampling, J. Amer. Statist. Assoc. 87 (1992), pp. 376–382] method has been considered. We conclude that the chi-squared distance between the design weights and the calibrated weights equals the square of the standardized Z-score obtained by the difference between the known population total of the auxiliary variable and its corresponding Horvitz and Thompson [A generalization of sampling without replacement from a finite universe, J. Amer. Statist. Assoc. 47 (1952), pp. 663–685] estimator divided by the sample standard deviation of the auxiliary variable to obtain the linear regression estimator in survey sampling.     

Calibration Estimator of a Rare Sensitive Attribute with Poisson Distribution

In this paper we consider the calibration procedure for a rare sensitive attribute with Poisson distribution which suggested by Land et al. (2012) using auxiliary information associated with the variable of interest. In the calibration procedure, we can use auxiliary information such as socio-demographical variables for the respondents of rare sensitive attribute questions from an external source, and then this estimator can be improved with respect to the problems of non coverage or non response. From the efficiency comparison study, we show that the calibrated Poisson RR estimators are more efficient than that of Land et al. (2012), when the known population cell and marginal counts of auxiliary information are used for the calibration procedure.     

Estimation of finite population mean in simple and stratified random sampling using two auxiliary variables

We propose an improved difference-cum-exponential ratio type estimator for estimating the finite population mean in simple and stratified random sampling using two auxiliary variables. We obtain properties of the estimators up to first order of approximation. The proposed class of estimators is found to be more efficient than the usual sample mean estimator, ratio estimator, exponential ratio type estimator, usual two difference type estimators, Rao (1991) estimator, Gupta and Shabbir (2008) estimator, and Grover and Kaur (2011) estimator. We use six real data sets in simple random sampling and two in stratified sampling for numerical comparisons.