An improved class of robust ratio estimators by using the minimum covariance determinant estimation

Bulut, Hasan; Zaman, Tolga

doi:10.1080/03610918.2019.1697818

Cited by 21 publications

(18 citation statements)

References 9 publications

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“…We proposed two different estimators for simple random sampling in the study. The first estimators are as given in (15). The MSE of these estimators is given in (16).…”

Section: Applicationsmentioning

confidence: 99%

“…Zaman and Bulut [14] proposed ratio-type estimators using robust regression estimators and robust covariance matrices for stratified random sampling. Bulut and Zaman [15] presented the ratio-type estimators utilizing MCD estimates. Zaman and Bulut [16] provided the ratio estimators for population variance considering MCD and MVE robust covariance estimates, both simple and stratified random sampling.…”

Section: Introductionmentioning

confidence: 99%

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A new class of robust ratio estimators for finite population variance

Zaman

Bulut

2022

Scientia Iranica

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It is a general practice to use robust estimates to improve ratio estimators using functions of the parameters of an auxiliary variable. In this study, a new class of robust estimators based upon the minimum covariance determinant (MCD) and the minimum volume ellipsoid (MVE) robust covariance estimates have been suggested for estimating population variance in the presence of outlier values in the data set for the simple random sampling. The expression for the mean square error (MSE) of the proposed class of estimators is derived from the first degree of approximation. The efficiency of the proposed class of robust estimators is compared with some competing estimators discussed in the literature, and found that proposed estimators are better than other mentioned estimators here. In addition, real data set and simulation studies are performed to present the efficiencies of the estimators. We demonstrate theoretically and numerically that the proposed class of estimators performs better than all other competitor estimators under all situations.

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“…We proposed two different estimators for simple random sampling in the study. The first estimators are as given in (15). The MSE of these estimators is given in (16).…”

Section: Applicationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A new class of robust ratio estimators for finite population variance

Zaman

Bulut

2022

Scientia Iranica

Self Cite

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“…However, the problems of effects of outliers on regression slopes were not considered. Recently, the concept of using robust regression slopes has been extended to modification of variance estimators, estimation in stratified and double sampling schemes etc (See Bulut and Zaman [74], Zaman and Bulut [75], Zaman and Bulut [76,77], Zaman and Bulut [78]. This current study focused on the modification of robust regression estimators using robust non-conventional measures (Gini's mean, Downton's method, and probability weighted moment) and robust regression slopes simultaneously to address the effect of outliers on auxiliary functions and regression slopes respectively.…”

Section: Introductionmentioning

confidence: 99%

On the Efficiency of Modified Regression-type Estimators Using Robust Regression Slopes and Non-conventional Measures of Dispersion

Audu

Gidado

Dauran

et al. 2022

ARJOM

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Supplementary variables associated with the study variables have been identified to be helpful in improving the efficiency of ratio, product and regression estimators both at planning and estimation stages. The existing regression-based estimators are functions of regression slopes and known auxiliary variables which are sensitive to outliers. Zaman & Bulut [1] and Zaman [2] addressed the issue of regression slopes in the aforementioned estimators using robust regression slopes like Huber-M, Hampel-M, Least Trimmed Squares (LTS) and Least Absolute Deviation (LAD). However, their estimators still utilized known auxiliary functions which are also sensitive to outliers or extreme values. Similarly, Yadav and Zaman [3] suggested non-conventional robust parameters of auxiliary variable which are robust against outliers. However, the problems of effects of outliers on regression slopes were not considered. In this study, the estimators of Zaman & Bulut [1] and Zaman [2] estimators were modified using robust non-conventional measures and Yadav and Zaman [3] estimators were modified using robust regression slopes. The properties (Biases and MSEs) of the modified estimators were derived up to the first order of approximation using Taylor series approach. The efficiency conditions of the proposed estimators over the existing estimators considered in the study were established. The empirical studies were conducted using stimulation data to investigate the efficiency of the proposed estimators over the efficiency of the existing estimators. The results revealed that the proposed estimators have minimum MSEs and higher PREs among all the competing estimators for the simulated populations in the study. This implies that the proposed estimators are more efficient and can produce better estimate of the population mean compared to other existing estimators considered in the study.

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“…Zaman 30 and Zaman and Bulut 31 introduced improved and modified ratio estimators based on some robust regression methods. Bulut and Zaman 32 enhanced the efficiency of ratio estimators by adopting the minimum covariance determinant technique. Zaman and Bulut 33 have further improved the efficacy of the estimators suggested by Bulut and Zaman 32 under stratified sampling.…”

Section: Introductionmentioning

confidence: 99%

“…Bulut and Zaman 32 enhanced the efficiency of ratio estimators by adopting the minimum covariance determinant technique. Zaman and Bulut 33 have further improved the efficacy of the estimators suggested by Bulut and Zaman 32 under stratified sampling. Abid et al 34 proposed an improved and robust class of ratio estimators using various robust measures of dispersion.…”

Section: Introductionmentioning

confidence: 99%

On enhanced exponential‐cum‐ratio estimators using robust measures of location

Gulzar

Latif

Abid

et al. 2021

Concurrency and Computation

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Many studies are mainly concerned with the estimation of finite population mean and the well-known preferences for it are ratio estimators. This article offers a remedy for improvement in the estimation of a study variable, based on supplementary information related to dual auxiliary variables in the context of simple random sampling without replacement scheme. We proposed two new general classes of exponential-cum-ratio estimators to estimate a finite population mean utilizing dual auxiliary variables with suitable combinations of the conventional and nonconventional measures. The expression for the mean square error (MSE) and theoretical conditions for proposed classes have been obtained for evaluation purposes. The performance of the proposed classes has been compared with existing estimators in terms of MSE. It is revealed that proposed estimators are more efficient than usual and existing estimators considered in this article. The simulation and robustness studies are also part of this article. Moreover, a variety of real data sets is also considered for an empirical study to support the theoretical results.

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An improved class of robust ratio estimators by using the minimum covariance determinant estimation

Cited by 21 publications

References 9 publications

A new class of robust ratio estimators for finite population variance

A new class of robust ratio estimators for finite population variance

On the Efficiency of Modified Regression-type Estimators Using Robust Regression Slopes and Non-conventional Measures of Dispersion

On enhanced exponential‐cum‐ratio estimators using robust measures of location

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