Efficient M-estimators with auxiliary information

This paper introduces a new class of M-estimators based on generalised empirical likelihood (GEL) estimation with some auxiliary information available in the sample. The resulting class of estimators is efficient in the sense that it achieves the same asymptotic lower bound as that of the efficient generalised method of moment (GMM) estimator with the same auxiliary information. The paper also shows that in case of smooth estimating equations the proposed estimators enjoy a small second order bias property compared to both efficient GMM and full GEL estimators. Analytical formulae to obtain bias corrected estimators are also provided. Simulations show that with correctly specified auxiliary information the proposed estimators and in particular those based on empirical likelihood outperform standard M and efficient GMM estimators both in terms of finite sample bias and efficiency. On the other hand with moderately misspecified auxiliary information estimators based on the nonparametric tilting method are typically characterised by the best finite sample properties.     

Improvement in Estimating the Population Median in Simple Random Sampling and Stratified Random Sampling Using Auxiliary Information

This paper deals with estimation of population median in simple and stratified random samplings by using auxiliary information. Auxiliary information is rarely used in estimating population median, although there have been many studies to estimate population mean using auxiliary information. In this study, we suggest some estimators using auxiliary information such as mode and range of an auxiliary variable and correlation coefficient. We also expand these estimators to stratified random sampling for combined and separate estimators. We obtain mean square error equations for all proposed estimators and find theoretical conditions. These conditions are also supported by using numerical examples.     

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.     

Some Classes of Estimators for Median Estimation in Survey Sampling

In this article, we have suggested some classes of estimators for estimating finite population median using information on an auxiliary variable. To study the properties of suggested classes of estimators under large sample approximation, a generalized class of estimators has been suggested with its properties. It has been shown that the suggested classes of estimators are more efficient than other existing estimators. The results have been illustrated through an empirical study.     

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

In this article, we propose a new class of estimators to estimate the finite population mean by using two auxiliary variables under two different sampling schemes such as simple random sampling and stratified random sampling. The proposed class of estimators gives minimum mean squared error as compared to all other considered estimators. Some real data sets are used to observe the performances of the estimators. We show numerically that the proposed class of estimators performs better as compared to all other competitor estimators.     

A generalized class of estimators under two-phase stratified sampling for non response

In this paper, we propose a generalized class of estimators for finite population mean using two auxiliary variables in two-phase stratified sampling for non response. We identify 17 estimators as special cases of the proposed class of estimators. Expressions for the bias and mean squared error (MSE) of estimators are obtained up to first order of approximation. A data set is used for efficiency comparisons.     

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

In this paper, we suggest regression-type estimators for estimating the Bowley's 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 Bowley's 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.     

An Improved Class of Estimators for the General Population Parameters Using Auxiliary Information

This article suggests an improved class of estimators for estimating the general population parameter using information on an auxiliary variable. The properties of the suggested class of estimators have been studied under large sample approximation. The general results are then applied to estimate the population coefficient of variation of study variable using auxiliary information. An empirical study is given in support of the theoretical results.     

Improved estimator of population total in PPS sampling

In this paper, we have considered an estimation of the population total Y of the study variable y, making use of information on an auxiliary variable x. A class of estimators for the population total Y using transformation on both the variables study as well as auxiliary has been suggested based on the probability proportional to size with replacement (PPSWR). In addition to many the usual PPS estimator, Reddy and Rao's (1977) estimator and Srivenkataramana and Tracy's (1979, 1984, 1986) estimators are shown to be members of the proposed class of estimators. The variance of the proposed class of estimators has been obtained. In particular, the properties of 75 estimators based on different known population parameters of the study as well as auxiliary variables have been derived from the proposed class of estimators. In support of the present study, numerical illustrations are given.     

Quantile Estimation in the Presence of Auxiliary Information under Negatively Associated Samples

In this article, we apply the empirical likelihood technique to propose a new class of quantile estimators in the presence of some auxiliary information under negatively associated samples. It is shown that the proposed quantile estimators are asymptotically normally distributed with smaller asymptotic variances than those of the usual quantile estimators. It is also shown that blocking technique is an useful tool in estimating asymptotic variance under negatively associated samples, which makes it possible to construct normal approximation based confidence intervals for quantiles.     

A class of estimators using auxiliary information in sample surveys

A large class of estimators is considered for the mean of a finite population using information on an auxiliary variable. It is shown that members of this class of estimators are asymptotically no more efficient than the linear regression 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.     

Distribution estimation with auxiliary information for missing data

There is much literature on statistical inference for distribution under missing data, but surprisingly very little previous attention has been paid to missing data in the context of estimating distribution with auxiliary information. In this article, the auxiliary information with missing data is proposed. We use Zhou, Wan and Wang's method (2008) to mitigate the effects of missing data through a reformulation of the estimating equations, imputed through a semi-parametric procedure. Whence we can estimate distribution and the τth quantile of the distribution by taking auxiliary information into account. Asymptotic properties of the distribution estimator and corresponding sample quantile are derived and analyzed. The distribution estimators based on our method are found to significantly outperform the corresponding estimators without auxiliary information. Some simulation studies are conducted to illustrate the finite sample performance of the proposed estimators.     

Penalized calibration in survey sampling: Design-based estimation assisted by mixed models

Calibration techniques in survey sampling, such as generalized regression estimation (GREG), were formalized in the 1990s to produce efficient estimators of linear combinations of study variables, such as totals or means. They implicitly lie on the assumption of a linear regression model between the variable of interest and some auxiliary variables in order to yield estimates with lower variance if the model is true and remaining approximately design-unbiased even if the model does not hold. We propose a new class of model-assisted estimators obtained by releasing a few calibration constraints and replacing them with a penalty term. This penalization is added to the distance criterion to minimize. By introducing the concept of penalized calibration, combining usual calibration and this ‘relaxed’ calibration, we are able to adjust the weight given to the available auxiliary information. We obtain a more flexible estimation procedure giving better estimates particularly when the auxiliary information is overly abundant or not fully appropriate to be completely used. Such an approach can also be seen as a design-based alternative to the estimation procedures based on the more general class of mixed models, presenting new prospects in some scopes of application such as inference on small domains.     

Calibration estimation in dual-frame surveys

Survey statisticians make use of auxiliary information to improve estimates. One important example is calibration estimation, which constructs new weights that match benchmark constraints on auxiliary variables while remaining “close” to the design weights. Multiple-frame surveys are increasingly used by statistical agencies and private organizations to reduce sampling costs and/or avoid frame undercoverage errors. Several ways of combining estimates derived from such frames have been proposed elsewhere; in this paper, we extend the calibration paradigm, previously used for single-frame surveys, to calculate the total value of a variable of interest in a dual-frame survey. Calibration is a general tool that allows to include auxiliary information from two frames. It also incorporates, as a special case, certain dual-frame estimators that have been proposed previously. The theoretical properties of our class of estimators are derived and discussed, and simulation studies conducted to compare the efficiency of the procedure, using different sets of auxiliary variables. Finally, the proposed methodology is applied to real data obtained from the Barometer of Culture of Andalusia survey.     

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.     

Estimation of population distribution function involving measurement error in the presence of non response

Abstract

This article addresses the problem of estimating population distribution function for simple random sampling in the presence of non response and measurement error together. We suggest a general class of estimators for estimating the cumulative distribution function using the auxiliary information. The expressions for the bias and mean squared error are derived up to the first order of approximation. The performance of the proposed class of estimators is compared with considered estimators both theoretically and numerically. A real data set is used to support the theoretical findings.     

A general class of chain estimators for ratio and product of two means of a finite population

This paper proposes a class of estimators for estimating ratio and product of two means of a finite population using information on two auxiliary characters. Asymptotic expression to terms of order 0(n^-1) for bias and mean square error (MSE) of the proposed class of estimators are derived. Optimum conditions are obtained under which the proposed class of estimators has the minimum MSE. An empirical study is carried out to compare the performance of various estimators of ratio with the conventional estimators.     

Calibration for Randomized Response Estimators

In the present article, we consider the calibration procedure for the Warner's and Mangat–Singh's (:M–S) randomized response survey estimators using auxiliary information associated with the variable of interest. In the calibration procedure, we can use auxiliary information such as age, gender, and income for the respondents of RR questions from an external source, and then the classical RR estimators can be improved with respect to the problems of noncoverage or nonresponse. From the efficiency comparison study, we show that the calibration estimators are more efficient than those of Warner's and Mangat-Singh's when the known population cell and marginal counts of auxiliary information are used for the calibration procedure.     

Improvement over variance estimation using auxiliary information in sample surveys

This paper addresses the problem of estimating the population variance S²_y of the study variable y using auxiliary information in sample surveys. We have suggested a class of estimators of the population variance S²_y of the study variable y when the population variance S²_x of the auxiliary variable x is known. Asymptotic expressions of bias and mean squared error (MSE) of the proposed class of estimators have been obtained. Asymptotic optimum estimators in the proposed class of estimators have also been identified along with its MSE formula. A comparison has been provided. We have further provided the double sampling version of the proposed class of estimators. The properties of the double sampling version have been provided under large sample approximation. In addition, we support the present study with aid of a numerical illustration.