Assessment of correlated measurement errors in presence of missing data using ranked set sampling

Anoop Kumar; Shashi Bhushan; Abdullah Mohammed Alomair; Anoop Kumar; Shashi Bhushan; Abdullah Mohammed Alomair

doi:10.3934/math.2025449

AIMS Mathematics

2025, Volume 10, Issue 4: 9805-9831. doi: 10.3934/math.2025449

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Research article

Assessment of correlated measurement errors in presence of missing data using ranked set sampling

1.
Department of Statistics, Central University of Haryana, Mahendergarh, Haryana 123031, India
2.
Department of Statistics, University of Lucknow, Lucknow, Uttar Pradesh, 226007, India
3.
Department of Quantitative Methods, School of Business, King Faisal University, Al-Ahsa 31982, Saudi Arabia

Received: 28 January 2025 Revised: 26 March 2025 Accepted: 21 April 2025 Published: 27 April 2025
MSC : 62D05, 62D10

A miniscule amount of work was done for the assessment of measurement errors in the existence of missing data using a few sampling techniques, while no work was available for the assessment of correlated measurement errors in the existence of missing data. This study aimed to propose some general imputation methods and the corresponding resultant estimators in the existence of missing data under ranked set sampling, provided the data was contaminated with the correlated measurement errors. The mean square error of the developed resultant estimators was established to the first order approximation. The potency of the developed imputation methods and corresponding resultant estimators was assessed by a comprehensive simulation experiment relying on a hypothetically created population. The findings indicated that the proposed imputation methods and the resultant estimators surpassed the traditional imputation methods and the resultant estimators. In addition, a real data application of the proposed imputation methods was also provided.
- correlated measurement errors,
- searls type power ratio imputation methods,
- searls type power ratio estimators,
- simulation
Citation: Anoop Kumar, Shashi Bhushan, Abdullah Mohammed Alomair. Assessment of correlated measurement errors in presence of missing data using ranked set sampling[J]. AIMS Mathematics, 2025, 10(4): 9805-9831. doi: 10.3934/math.2025449

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Abstract

A miniscule amount of work was done for the assessment of measurement errors in the existence of missing data using a few sampling techniques, while no work was available for the assessment of correlated measurement errors in the existence of missing data. This study aimed to propose some general imputation methods and the corresponding resultant estimators in the existence of missing data under ranked set sampling, provided the data was contaminated with the correlated measurement errors. The mean square error of the developed resultant estimators was established to the first order approximation. The potency of the developed imputation methods and corresponding resultant estimators was assessed by a comprehensive simulation experiment relying on a hypothetically created population. The findings indicated that the proposed imputation methods and the resultant estimators surpassed the traditional imputation methods and the resultant estimators. In addition, a real data application of the proposed imputation methods was also provided.

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