Ratio and product methods of estimation of population mean in the presence of correlated measurement errors

Shalabh,; Tsai, Jia-Ren

doi:10.1080/03610918.2016.1165845

Cited by 35 publications

(59 citation statements)

References 12 publications

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“… equal to zero we can obtain the MSE without observational error which is the same as obtained by [25]. From (7) and 22…”

Section: Vsymentioning

confidence: 75%

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Computing the Average Body Mass Index: A Study with Systematic Sampling Using Auxiliary Information

Vishwakarma¹,

Singh²,

Singh³

2020

Preprint

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Background: The use of body mass index (BMI) could lead to over/under estimation of fat mass percentage. Systematic sampling is to be applied only if the given population is logically homogeneous, because systematic sample units are uniformly distributed over the population. The method of estimation for mean of the study variable under systematic sampling using auxiliary information has been proposed to estimate the body mass index (BMI).Methods: The measures of different body parts are taken as auxiliary variables. The observation available on different body parts are assumed to be recorded with observational error. Thus we also propose method of estimation for mean in the presence of observational error. Numerical study has been done to reveal the efficacy of the proposed procedure for estimation of mean. Simulation study has also been done to demonstrate the effect of observational error on the estimation of body mass index.Results: The properties of the proposed estimation method have been derived under large sampling approximation and obtained the conditions under which proposed method are more efficient. Conclusions: The study provides an easy approach and simplest way to obtain the BMI estimate with and without observational error. Thus the suggested method may be used by statistician for this problem and for many others similar problem in the estimation of mean.

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“… equal to zero we can obtain the MSE without observational error which is the same as obtained by [25]. From (7) and 22…”

Section: Vsymentioning

confidence: 75%

“…[3,4,5,6] have discussed the observational error in the context of linear and non-linear regression models. [7,8,9,10,11] have studied the observational error in the estimation of ratio, product and regression methods of estimation.…”

Section: Introductionmentioning

confidence: 99%

Computing the Average Body Mass Index: A Study with Systematic Sampling Using Auxiliary Information

Vishwakarma¹,

Singh²,

Singh³

2020

Preprint

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show abstract

“…Chandhok and Han 6 have investigated the ratio estimators under SRSWOR and Midzuno schemes when observational errors are present. Shalabh and Tsai 7 investigated ratio estimators in SRS when both observations

X

(auxiliary) and

Y

(study) are subject to correlated observational errors. Later on Gregorre and Salas, 8 Allen et al 9 have studied the impact of observational errors while estimating the mean.…”

Section: Introductionmentioning

confidence: 99%

A computational framework for estimation of mean in presence of observational error

Vishwakarma

Singh

Kumar

2022

Concurrency and Computation

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This article presents a computational framework for estimation of the mean in two-phase sampling mechanism using multi-auxiliary variables when observational errors are observed in sample data. A competent class of estimators is proposed which encompasses several existing estimation techniques under observational error. The properties of the proposed class of estimators have been explored under large sample approximation using the Taylor series expansions method. A strive is done to obtain the optimum sample sizes for a certain cost of the survey. The impact of observational errors is assessed over the mean square error of the estimators. The simulation study is demonstrated to reflect the dominant nature of the proposed class of estimators over the existing one.

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“…Under the simple random sampling scheme, ratio and product estimation techniques are widely used. For more details about these two estimation techniques, studies by Cochran [3], Murthy [4], Singh [5], and Shalabh and Tsai [6] can be referred. Furthermore, there is a wealth of literature on ratio estimators for population mean.…”

Section: Introductionmentioning

confidence: 99%

Minimum Covariance Determinant-Based Quantile Robust Regression-Type Estimators for Mean Parameter

Shahzad

Al‐Noor

Afshan

et al. 2021

Mathematical Problems in Engineering

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Robust regression tools are commonly used to develop regression-type ratio estimators with traditional measures of location whenever data are contaminated with outliers. Recently, the researchers extended this idea and developed regression-type ratio estimators through robust minimum covariance determinant (MCD) estimation. In this study, the quantile regression with MCD-based measures of location is utilized and a class of quantile regression-type mean estimators is proposed. The mean squared errors (MSEs) of the proposed estimators are also obtained. The proposed estimators are compared with the reviewed class of estimators through a simulation study. We also incorporated two real-life applications. To assess the presence of outliers in these real-life applications, the Dixon chi-squared test is used. It is found that the quantile regression estimators are performing better as compared to some existing estimators.

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Ratio and product methods of estimation of population mean in the presence of correlated measurement errors

Cited by 35 publications

References 12 publications

Computing the Average Body Mass Index: A Study with Systematic Sampling Using Auxiliary Information

Computing the Average Body Mass Index: A Study with Systematic Sampling Using Auxiliary Information

A computational framework for estimation of mean in presence of observational error

Minimum Covariance Determinant-Based Quantile Robust Regression-Type Estimators for Mean Parameter

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