Improved estimation of population parameter of in the existence of nonresponse using auxiliary information

Badr Aloraini; Badr Aloraini

doi:10.3934/math.2025558

AIMS Mathematics

2025, Volume 10, Issue 5: 12312-12342. doi: 10.3934/math.2025558

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Research article Topical Sections

Improved estimation of population parameter of in the existence of nonresponse using auxiliary information

Badr Aloraini ^,

Department of Mathematics, College of Science and Humanities, Shaqra University, 11961, Shaqra, Saudi Arabia

Received: 01 March 2025 Revised: 26 April 2025 Accepted: 06 May 2025 Published: 27 May 2025
MSC : 03H10, 37N40, 62P20, 68T07, 68T09, 91G15, 91G30

The issue of survey nonresponse causes substantial effects on the reliability, together with validity of study findings. This research develops precise estimation methods for two distinct nonresponse situations: when nonresponse happens to primary survey variables like the number of students, and when nonresponse includes survey variables together with the accompanying auxiliary variables. The proposed estimators receive full a performance assessment through derived equations for bias and mean square error (MSE) based on first-order approximation. The accuracy and reliability assessment depends heavily on MSE calculations, since this method effectively merges systematic error measurements with random error measurements. The MSE values of different estimators receive numerical evaluation through a comparative analysis under equivalent operational conditions for assessing proposed estimator performance outcomes. The research seeks to find the estimator with the minimal MSE because this selection results in the most trustworthy estimates under nonresponse conditions. All the findings from this study create important guidelines for building educational survey designs.
- auxiliary variables,
- bias,
- efficiency,
- estimation of mean,
- mean squared error,
- nonresponse
Citation: Badr Aloraini. Improved estimation of population parameter of in the existence of nonresponse using auxiliary information[J]. AIMS Mathematics, 2025, 10(5): 12312-12342. doi: 10.3934/math.2025558

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Abstract

The issue of survey nonresponse causes substantial effects on the reliability, together with validity of study findings. This research develops precise estimation methods for two distinct nonresponse situations: when nonresponse happens to primary survey variables like the number of students, and when nonresponse includes survey variables together with the accompanying auxiliary variables. The proposed estimators receive full a performance assessment through derived equations for bias and mean square error (MSE) based on first-order approximation. The accuracy and reliability assessment depends heavily on MSE calculations, since this method effectively merges systematic error measurements with random error measurements. The MSE values of different estimators receive numerical evaluation through a comparative analysis under equivalent operational conditions for assessing proposed estimator performance outcomes. The research seeks to find the estimator with the minimal MSE because this selection results in the most trustworthy estimates under nonresponse conditions. All the findings from this study create important guidelines for building educational survey designs.

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