On calibrated weights in stratified sampling

Calibration approach is widely used survey sampling that incorporates auxiliary information to increase the precision of survey estimates. In this manuscript, we propose two new calibration estimators of population mean in stratified sampling, using the known auxiliary information on mean and coefficient of variation in each stratum. A numerical example is presented to illustrate the application and computational details of the proposed calibration estimators. Moreover, a simulation study is carried out to compare the performance of the proposed calibration estimators.

An improved ratio-type calibrated estimator was developed using the logarithmic mean in the calibration constraint for the stratified random sampling scheme. The proposed estimator was extended in the case of stratified double sampling and compared with the estimators given by Tracy et al. (2003) together its ratio-type estimators, as well as Nidhi et al. (2017) and Khare et al. (2022). A simulation study was also carried out on both a real and artificial dataset in order to evaluate the performance of the proposed estimator compared to the existing estimators.

In this paper we have suggested a general procedure for estimating the population mean in stratified sampling using auxiliary information. A general class of estimators is defined with its properties under large sample approximation. In particular, various classes of estimators are identified as particular member of the suggested class. The correct version of the mean squared error of Kadilar and Cingi (2005) class of estimators is derived. It has been shown that the proposed class of estimators is better than Kadilar and Cingi (2005) estimator, usual unbiased estimator, usual combined ratio estimator yRC, combined product estimator yPC, Gangde et al. (1993) type estimator and Searls (1964) type estimator. Numerical illustration is given in support of present study.

In this article, a combined general family of estimators is proposed for estimating finite population mean of a sensitive variable in stratified random sampling with non-sensitive auxiliary variable based on randomized response technique. Under stratified random sampling without replacement scheme, the expression of bias and mean square error (MSE) up to the first-order approximations are derived. Theoretical and empirical results through a simulation study show that the proposed class of estimators is more efficient than the existing estimators, i.e., usual stratified random sample mean estimator, Sousa et al (2014) ratio and regression estimator of the sensitive variable in stratified sampling.

ABSTRACTThis 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.

Ranked set sampling is an alternative to simple random sampling, which uses the least amount of money and time. The ranked set sampling (RSS) is modified to obtain a more efficient and cost-effective estimator of population parameters. This paper aims to bring a more efficient and cost-effective design than stratified ranked set sampling and simple random sampling. In some distributions, the suggested method used fewer sample units than stratified ranked set sampling and gives a more efficient estimation of population parameters. In symmetric distributions, the proposed design, called "partial stratified ranked set sampling" yields an unbiased estimator of the population mean. The design is illustrated with practical data of COVID-19 confirmed cases.

This paper considers the problem of estimating the population mean of the study variable when auxiliary information is not available and proposes new calibration approach alternative to the recent existing calibration estimators for estimating population mean of the study variable using two auxiliary variables in stratified two-phase sampling. The theory of new calibration estimation is given and optimum weights are derived under two-phase sampling approach. A simulation study is carried out to performance of the proposed calibration estimator with other existing calibration estimators. The results demonstrate that the proposed calibration estimator is more efficient than other existing calibration estimators of the population mean in stratified two-phase sampling.

ABSTRACTCalibration estimation improves the precision of the estimates of population parameters by incorporating specified auxiliary information. A class of calibration estimators has been proposed for estimating the population mean by making use of a set of calibration constraints in stratified sampling. The estimator of variance of the proposed calibration estimator of the mean is derived using a lower level calibration approach. The idea is extended for stratified double sampling. A simulation study is used to evaluate the performances of the proposed estimators by comparing them with the similar estimators developed by Tracy, Singh and Arnab (2003) based on different sets of calibration constraints.

Adapting a global stratified random sample for regional estimation of forest cover change derived from satellite imagery

Since 1967, when the Polish State Forests were first inventoried, a continuous increase in the volume of growing stock has been recorded. This increase in timber resources is mainly the result of sustainable forest management. However, during this time period inventory methods have been changed a few times and this may have affected the estimates of of wood resources. Since 2011 new instructions have been in place for forest management plans in the Polish State Forests. Despite this, the method of taking forest inventories remained consistent with the previous guidelines. This should allow us to consider changes in the volume of growing stock in relation to inventory methods and their accuracy. In this paper, the results of growing stock estimations based on two assessments made using stratified random sampling are compared. After five years of inventories made for forest management plans, 422 sample plots in two forest districts were measured within 15 strata. Predicted age classes structure at the beginning of successive management plans was used to determine new strata. Data from two inventories were compared on the basis of age class. In addition, data from the State Forests Information System i.e. updated stand level inventory data (on felling and tree growth) were analyzed. Comparing data from the two inventories, in three of seven age classes there was a decrease in the volume of growing stock after a five year period. We found no rational explanation for this. The extent of felling in the analyzed stand was very low, as confirmed by data from State Forests database. However, the largest decrease in volume was 1.5%, whereas the accuracy of growing stock assessment of discussed age class was estimated at some 9% in 2006 and 8% in 2011. Hence, from statistical viewpoint there was no differences between the results of both inventories. However, the differences between volume of growing stock of examined age classes, updated in the Information System of the State Forests and results of assessments by stratified sampling are less than 95% confidence intervals for means of samples. Because of that, updated information could be used in the long term management planning. The results clearly suggest that changes of growing stock, estimated as a difference between two assessments, should be interpreted in conjunction with the accuracy of these inventories. The accuracy of sampling should be also taken into account when creating management plans.

This article considers simultaneous estimation of means from several strata, where each stratum contains a finite number of elements. For example, quite often estimates of annual incomes, unemployment rates, and so forth must be made simultaneously for many areas. Our results find application in small area estimation where very few samples are available from an individual area, and an estimate of a certain area mean or simultaneous estimates of several area means can be improved by incorporating information from similar neighboring areas. Ghosh and Meeden (1986) considered empirical Bayes estimation of the finite population mean assuming a normal superpopulation model. Their estimators generalize automatically when one estimates a vector of stratum means. This article relaxes the normality assumption and assumes instead that the posterior expectation of any stratum mean is a linear function of the sample observations. This is the so-called “posterior linearity” property as described in Ericson (1...

Auxiliary variable is commonly used in survey sampling to improve the precision of estimates. Whenever there is auxiliary information available, the researchers want to utilize it in the method of estimation to obtain the most efficient estimator. Stratified simple random sampling (SSRS) is used in certain types of surveys because it combines the conceptual simplicity of simple random sampling (SRS) with potentially significant gains in efficiency. It is a convenient technique to use whenever we wish to ensure that our sample is representative of the, population and also to obtain separate estimates for parameters of each sub domain of the population. Stratified Ranked Set Sampling combines the advantages of Stratification and Ranked set sampling (RSS) to obtain an unbiased estimator for the population mean, with potentially significant gains in efficiency. Under Stratified ranked set sampling scheme, we have suggested two general estimators using power transformation to estimate the population mean of the study variable. These methods are highly beneficial to the estimation based on Stratified Simple Random Sampling (SSRS). The first order approximation to the bias and mean square error (MSE) of the proposed estimators are obtained. Theoretically, it is shown that these suggested estimators are more efficient than the estimators in Stratified simple random sampling. A numerical illustration is also included to demonstrate the merits of the proposed estimator using SRSS over the corresponding estimators in SSRS.

In stratified random sampling, Ahsan et al. [Mixed allocation in stratified sampling. Aligarh J Stat. 2005;25:87–97] introduced the concept of ‘Mixed allocation’ for fixed cost by minimizing the variance of the stratified sample mean which was based on the work of Clark and Steel [Optimum allocation of sample to strata and stages with simple additional constraints. Statistician. 2000;49(2):197–207] for two-stage univariate sampling design. The present manuscript studies the problem of obtaining a ‘compromise mixed allocation’ in multivariate stratified sampling using Fuzzy Programming Technique. To exhibit the application of the defined approach, a numerical illustration is considered and solved using Lingo 13.0. In order to demonstrate the superiority of proposed approach, the obtained results have been compared with four other existing approaches.

Kappa coefficient is a popular statistic to measure the agreement between the classifications of two raters. The estimator of the coefficient and its variance are approximately satisfied by a simple random sampling method. To get more efficient results for confidence interval estimation of kappa, stratified random sampling method can also be used, alternatively. In this study, a bootstrap method under stratified sampling is suggested to use to estimate the confidence interval of kappa coefficient. The results are discussed over three data sets.

This paper presents the results of a limited investigation which brings into focus the difficulties encountered in developing exact distribution-free methods for stratified simple random sampling. It is shown that exact distribution-free confidence intervals for a population median can be obtained from a stratified sample under very special circumstances. The principal result concerns the order statistics of the combined separate strata samples, where proportional allocation is employed. It is proved that a pair of symmetric order statistics provides a confidence interval for the population median whose confidence coefficient is not less than the confidence coefficient obtained from the corresponding order statistics of a random sample of the same total size drawn from the entire population. Furthermore, it is shown by means of a numerical example that this result necessarily holds only when proportional allocation is employed.