Estimators In Stratified Sampling Research Articles

Some Improved Classes of Estimators in Stratified Sampling Using Bivariate Auxiliary Information

This manuscript considers some improved combined and separate classes of estimators of population mean using bivariate auxiliary information under stratified simple random sampling. The expressions of bias and mean square error of the proposed classes of estimators are determined to the first order of approximation. It is exhibited that under some particular conditions, the proposed classes of estimators dominate the existing prominent estimators. The theoretical findings are supported by a simulation study performed over a hypothetically generated population.

A New Exponential Factor-Type Estimator for Population Distribution Function Using Dual Auxiliary Variables under Stratified Random Sampling

In this paper, we propose a generalized class of exponential-type estimators for estimating the finite population distribution function using dual auxiliary variables under stratified sampling. The biases and mean squared errors (MSEs) of the proposed class of estimators are derived up to the first order of approximation. The empirical and theoretical study of comparisons is discussed. Four populations are taken for the support of the theoretical findings. It is observed that the proposed class of estimators performs better as compared to all other considered estimators in stratified sampling.

Variance estimation in stratified adaptive cluster sampling

Abstract In many sampling surveys, the use of auxiliary information at either the design or estimation stage, or at both these stages is usual practice. Auxiliary information is commonly used to obtain improved designs and to achieve a high level of precision in the estimation of population density. Adaptive cluster sampling (ACS) was proposed to observe rare units with the purpose of obtaining highly precise estimations of rare and specially clustered populations in terms of least variances of the estimators. This sampling design proved to be more precise than its more conventional counterparts, including simple random sampling (SRS), stratified sampling, etc. In this paper, a generalised estimator is anticipated for a finite population variance with the use of information of an auxiliary variable under stratified adaptive cluster sampling (SACS). The bias and mean square error expressions of the recommended estimators are derived up to the first degree of approximation. A simulation study showed that the proposed estimators have the least estimated mean square error under the SACS technique in comparison to variance estimators in stratified sampling.

Memory Type Ratio and Product Estimators in Stratified Sampling

The exponential weighted moving average (EWMA) statistic is utilized the past information along with the present to enhance the efficiency of the estimators of the population parameters. In this study, the EWMA statistic is used to estimate the population mean with auxiliary information. The memory type ratio and product estimators are proposed under stratified sampling (StS). Mean square errors (MSE) expressions and relative efficiencies of the proposed estimators are derived. An extensive simulation study is conducted to evaluate the performance of the proposed estimators. An empirical study is presented based on real-life data that supports the findings of the simulation study.

On calibrated weights in stratified sampling

In this paper, we propose a calibration estimator of population mean in stratified sampling using the known mean and variance information from multi-auxiliary variables. The problem of determining the optimum calibrated weights is formulated as a Nonlinear Programming Problem (NLPP) that is solved using the Lagrange multiplier technique. Numerical example with real data is presented to illustrate the computational details of the proposed estimator. A comparison study is also carried out using real and simulated data to evaluate the performance and the usefulness of the proposed estimator. The study reveals that the proposed estimator with multi-auxiliary information is more efficient estimator of the population mean as it provides least estimated variance and highest gain in relative efficiency (RE). References Jean Claude Deville and Carl Erik Sarndal. Calibration estimators in survey sampling. Journal of the American statistical Association, 87(418):376–382, 1992. doi:10.1080/01621459.1992.10475217 . Victor M Estevao and Carl Erik Sarndal. Survey estimates by calibration on complex auxiliary information. International Statistical Review, 74(2):127–147, 2006. doi:110.1111/j.1751-5823.2006.tb00165.x Patrick J Farrell and Sarjinder Singh. Model-assisted higher-order calibration of estimators of variance. Australian and New Zealand Journal of Statistics, 47(3):375–383, 2005. doi:10.1111/j.1467-842X.2005.00402.x Wolfram Research, Inc. Mathematica, Version 11.3. Champaign, IL, 2018. Jong Min Kim, Engin A Sungur, and Tae Young Heo. Calibration approach estimators in stratified sampling. Statistics and probability letters, 77(1):99–103, 2007. doi:10.1016/j.spl.2006.05.015 Phillip S Kott. Using calibration weighting to adjust for nonresponse and coverage errors. Survey Methodology, 32(2):133, 2006. Dinesh K Rao. Mathematical programing in stratified random sampling. PhD thesis, School of Computing, Information and Mathematical Sciences, The University of the South Pacific, Fiji, February 2017. Dinesh K. Rao, Tokaua. Tekabu, and Mohammad G M Khan. New calibration estimators in stratified sampling. In Proceedings of Asia-Pacific World Congress on Computer Science and Engineering, pages 66–70. IEEE, 2016. Gurmindar K Singh, Dinesh K Rao, and Mohammed GM Khan. Calibration estimator of population mean in stratified random sampling. In Proceedings of Asia-Pacific World Congress on Computer Science and Engineering (APWC on CSE), pages 1–5. IEEE, 2014. Sarjindar Singh, Stephen Horn, and Frank Yu. Estimation of variance of general regression estimator: Higher level calibration approach. Survey Methodology, 24:41–50, 1998. Sarjinder Singh. Advanced Sampling Theory With Applications: How Michael Selected Amy, volume I and II. Kluwer Academic Publishers, Netherlands, 2003. Sarjinder Singh. On the calibration of design weights using a displacement function. Metrika, 75(1):85–107, 2012. doi:10.1007/s00184-010-0316-6 Sarjinder Singh, Stephen Horn, Sadeq Chowdhury, and Frank Yu. Theory and methods: Calibration of the estimators of variance. Australian and New Zealand Journal of Statistics, 41(2):199–212, 1999. doi:10.1111/1467-842X.00074 D S Tracy, S Singh, and R Arnab. Note on calibration in stratified and double sampling. Survey Methodology, 29(1):99–104, 2003. Changbao Wu and Randy R Sitter. A model-calibration approach to using complete auxiliary information from survey data. Journal of the American Statistical Association, 96(453):185–193, 2001. doi:10.1198/016214501750333054

Using a simulation analysis to evaluate the impact of crop mapping error on crop area estimation from stratified sampling

ABSTRACTTo analyze the efficiency of area estimations (i.e. estimation accuracy and variation of estimation) impacted by crop mapping error, we simulated error at eight levels for thematic maps using a stratified sampling estimation methodology. The results show that the estimation efficiency is influenced by the combination of the sample size and the error level. Evaluating the trade-offs between sample size and error level showed that reducing the crop mapping error level provides the most benefit (i.e. higher estimation efficiency). Further, sampling performance differed based on the heterogeneity of the crop area. The results demonstrated that the influence of increasing the error level on estimation efficiency is more detrimental in heterogeneous areas than in homogeneous ones. Therefore, to obtain higher estimation efficiency, a larger sample size and lower error level or both are needed, especially in heterogeneous areas. We suggest that existing land-cover maps should first be used to determine the heterogeneity of the area. The appropriate sample size for these areas then can be determined according to all three factors: heterogeneity, expected estimation efficiency, and sampling budget. Overall, extending our understanding of the impacts of crop mapping error is necessary for decision making to improve our ability to effectively estimate crop area.

New calibration estimator based on two auxiliary variables in stratified sampling

ABSTRACTIn recent years, calibration estimation has become an important field of research in survey sampling. This paper proposes a new calibration estimator for the population mean in the presence of two auxiliary variables in stratified sampling. The theory of new calibration estimator is given and optimum calibration weights are derived. A simulation study is carried out to performance of the proposed calibration estimator over other existing calibration estimators. The results reveal that the proposed calibration estimators are more efficient than other existing calibration estimators in stratified sampling.

Calibration approach estimators in stratified sampling

Calibration is commonly used in survey sampling to include auxiliary information to increase the precision of the estimates of population parameter. In this paper, we newly propose various calibration approach ratio estimators and derive the estimator of the variance of the calibration approach ratio estimators in stratified sampling.

Improved Ratio Estimators in Stratified Sampling

SYNOPTIC ABSTRACTKADILAR 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.

Correction: Conditional Properties of Some Estimators in Stratified Sampling

Correction: Conditional Properties of Some Estimators in Stratified Sampling

Conditional Properties of Some Estimators in Stratified Sampling

Abstract The prediction properties of the stratified expansion estimator, the separate and combined ratio estimators, and the separate and combined regression estimators are studied under a model appropriate to a population stratified on a size variable. Several estimators of variance for each total estimator are considered, including standard ones from probability sampling theory, alternative choices derived from a superpopulation model, and the jackknife. The theory is tested in an empirical study using a real population. Earlier studies of the ratio and regression estimators under simple random sampling plans have illustrated that conditional properties of those estimators and of the linearization variance estimators that are often used with them can be much different and less desirable than unconditional properties. Whether similar results hold for stratified samples and estimators has been the subject of some debate. This article illustrates both theoretically and empirically that the use of stratifi...

Conditional Properties of Some Estimators in Stratified Sampling

Conditional Properties of Some Estimators in Stratified Sampling

A Nested Partitioning Procedure for Numerical Multiple Integration

Abstract : An algorithm is presented for adaptively partitioning a multidimensional coordinate space based on optimization of a scalar function of the coordinates. The goal is to construct a set of hyperrectangular regions, such that the variation of function values within each region is small. These regions are then used as the basis for a stratified sampling estimate of the definite integral of the function. (Author)