Dual Use Of Auxiliary Information Research Articles

Empirical distribution function based dual use of auxiliary information for the improved estimation of finite population mean

SummaryThis research primarily aims at the development of a new estimation scheme exploiting the argument of dual use of auxiliary information. The objectives are obtained by materializing the new family of estimators, where the dual use of Supplementary Information is substantiated with the launch of the empirical distribution function of the auxiliary variable. The comparative performance evaluation of the newly devised formation is enumerated with respect to the most efficient method, to the best of our knowledge till to date, of Haq et al. along with other promising families of Hussain and Haq and Grover and Kaur. The elaborative account of contemporary advents of the newly proposed family are documented throughout the article.

Modified estimators of finite population distribution function based on dual use of auxiliary information under stratified random sampling.

In survey sampling, information on auxiliary variables related to the main variable is often available in many practical problems. Since the mid-twentieth century, researchers have taken a keen interest in the use of auxiliary information due to its usefulness in estimation methods. The current study presents two new estimators for the distribution function of a finite population based on dual auxiliary variables. The new estimators can be used in situations where the researchers face some sort of complex data set. The mathematical equations for the bias and mean square error have been obtained for each proposed estimator. Besides, an empirical study simulation study has also been conducted to analyse the performance of estimators. It is found that the new suggested estimators of the distribution function of a finite population are more accurate than some of the existing estimators.

Dual Use of Auxiliary Information for Estimating the Finite Population Mean under the Stratified Random Sampling Scheme

In this paper, we proposed an improved family of estimators for finite population mean under stratified random sampling, which needed a helping variable on the sample mean and rank of the auxiliary variable. The expression of the bias and mean square error of the proposed and existing estimators are computed up to the first-order approximation. The estimators proposed in different situations were investigated and provided a minimum mean square error relative to all other estimators considered. Four actual data sets and simulation studies are carried out to observe the performance of the estimators. For simulation study, R software is used. The mean square errors of all four data sets are minimum and percent relative efficiencies are more than a hundred percent higher than the other existing estimators, which indicated the importance of the newly proposed family of estimators. From the simulation study, it is concluded that the suggested family of estimators achieved better results. We demonstrate theoretically and numerically that the proposed estimator produces efficient results compared to all other contend estimators in entire situations. Overall, we conclude that the performance of the family of suggested estimators is better than all existing estimators.

Optimality of ratio and regression type estimators using dual of auxiliary variable under non response

The present note addresses the problem of estimation of population mean in the presence of non response. We have proposed the difference and ratio type estimators in two distinct situations of non response using the dual of an auxiliary variable. Some conventional estimators like mean, ratio, product, power transformation, regression, difference, and some other difference type estimators are the special cases of the proposed estimators apart from being less efficient than proposed estimators in the respective situations.The present work can be considered as the efficient extension of a recent work that is based on the dual use of auxiliary information. The theoretical results are obtained under large sample approximation. A comparative study based on real and simulated data is conducted where the results are quite encouraging, providing the improvement over all the discussed works.

Estimation of finite population distribution function with dual use of auxiliary information under non-response.

In this paper, we propose two new families of estimators for estimating the finite population distribution function in the presence of non-response under simple random sampling. The proposed estimators require information on the sample distribution functions of the study and auxiliary variables, and additional information on either sample mean or ranks of the auxiliary variable. We considered two situations of non-response (i) non-response on both study and auxiliary variables, (ii) non-response occurs only on the study variable. The performance of the proposed estimators are compared with the existing estimators available in the literature, both theoretically and numerically. It is also observed that proposed estimators are more precise than the adapted distribution function estimators in terms of the percentage relative efficiency.

Difference-Type-Exponential Estimators Based on Dual Auxiliary Information Under Simple Random Sampling

Auxiliary information plays a vital role at the selection and/or estimation stage to achieve the efficient estimates of the unknown population parameters. Dual use of auxiliary information, one the original and second the ranks of the auxiliary variable help to increase the efficiency of the estimators. In this article, we proposed and evaluated the performance of difference-type-exponential estimators based on dual auxiliary information for population mean under simple random sampling. Mathematical expressions for the bias and the mean squared error of the proposed estimators are obtained. Three real-life data sets and Monte Carlo simulation studies are carried out for illustration. The results of the empirical and the simulation studies, in terms of mean square errors and percentage relative efficiencies indicate that the proposed estimators perform better as compared to their counterparts.

Estimation of General Parameter Under Stratified Adaptive Cluster Sampling Based on Dual Use of Auxiliary Information

Auxiliary information is mostly used together with study variable to enhance efficiency of estimators for population mean, total and variance. Thompson introduced adaptive cluster sampling as an appropriate sampling scheme for rare and clustered populations. In present article, difference-type and difference-cum-exponential-ratio-type estimators are presented utilizing two auxiliary variables for estimation of general parameter under stratified adaptive cluster sampling. Proposed estimators utilize auxiliary information in terms of ranks, variances and means of auxiliary variables in $h^{th}$ stratum. Expressions for bias and mean square error of proposed estimators are derived using first order of approximation. Numerical study is conducted to evaluate the performance of proposed estimators.

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

ABSTRACTWhenever 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.

On Effective Dual Use of Auxiliary Information in Variability Control Charts

During the last decade, variance control charts based on different sampling schemes have attracted research interest in the field of statistical process control. These charts used extra (auxiliary) information either for ranking of units or estimation rather than using it for both. The effectiveness of a control chart can be increased by utilizing the auxiliary information for dual purposes. This article is focused on developing a generalized structure of variance control charts based on dual use of auxiliary information under different sampling strategies and runs rules. The generalized structure mainly depends on three auxiliary information-based estimators with dual use of auxiliary information, three bivariate process distributions, and variety of sampling schemes. The performance of the proposed control charts is investigated by assessing the power curve. We have observed that the proposals of the study perform better than its complement. An application example is also provided for practitioners' concerns to monitor the stability of physicochemical parameter of groundwater. Copyright © 2015 John Wiley & Sons, Ltd.

On Dual Use of Auxiliary Information for Efficient Monitoring

In this study, a new idea has been proposed in statistical process control by making dual use of auxiliary information, that is, for ranking as well as at the estimation stage. The control charts are proposed based on regression estimator in three basic ranked set schemes, that is, ranked-set sampling (RSS), median RSS, and extreme RSS. The power of detection is used as a performance measure for evaluation and comparison of control charts. Comparisons revealed that the newly proposed charts (making dual use of auxiliary information) performed significantly better compared with the existing location charts. An illustrative example is also provided for the application of the proposed charts. Copyright © 2015 John Wiley & Sons, Ltd.