Non-parametric calibration estimation of distribution function under stratified random sampling

Abdullah Mohammed Alomair; Weineng Zhu; Usman Shahzad; Fawaz Khaled Alarfaj; Abdullah Mohammed Alomair; Weineng Zhu; Usman Shahzad; Fawaz Khaled Alarfaj

doi:10.3934/math.2025205

AIMS Mathematics

2025, Volume 10, Issue 2: 4457-4472. doi: 10.3934/math.2025205

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Non-parametric calibration estimation of distribution function under stratified random sampling

1.
Department of Quantitative Methods, School of Business, King Faisal University, Al-Ahsa 31982, Saudi Arabia
2.
Department of Statistics, University of Warwick, Coventry CV4 7AL, United Kingdom
3.
Department of Management Science, College of Business Administration, Hunan University, Changsha 410082, China
4.
Department of Management Information Systems, School of Business, King Faisal University, Al-Ahsa 31982, Saudi Arabia

Received: 06 December 2024 Revised: 15 February 2025 Accepted: 20 February 2025 Published: 28 February 2025
MSC : 62A86, 62G07

We introduced an innovative kernel-based nonparametric estimator for the cumulative distribution function (CDF) in finite populations, addressing the critical need to evaluate the proportion of values in a target variable that are less than or equal to specific thresholds. By leveraging auxiliary information under a stratified random sampling (StRS) framework, the proposed methodology employs multiple calibration constraints with a chi-square distance measure to derive calibrated weights, enhancing estimation efficiency. The estimators incorporate key descriptive measures of auxiliary variable, including the CDF and coefficient of variation, and tackle the challenge of bandwidth selection using advanced techniques such as plug-in selectors and cross-validation approaches. Simulation studies using datasets on apple production in Turkey and wheat production in Pakistan were conducted to assess the performance of the proposed estimators.
- cumulative distribution function (CDF),
- nonparametric,
- calibration approach,
- auxiliary information,
- stratified random sampling
Citation: Abdullah Mohammed Alomair, Weineng Zhu, Usman Shahzad, Fawaz Khaled Alarfaj. Non-parametric calibration estimation of distribution function under stratified random sampling[J]. AIMS Mathematics, 2025, 10(2): 4457-4472. doi: 10.3934/math.2025205

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Abstract

We introduced an innovative kernel-based nonparametric estimator for the cumulative distribution function (CDF) in finite populations, addressing the critical need to evaluate the proportion of values in a target variable that are less than or equal to specific thresholds. By leveraging auxiliary information under a stratified random sampling (StRS) framework, the proposed methodology employs multiple calibration constraints with a chi-square distance measure to derive calibrated weights, enhancing estimation efficiency. The estimators incorporate key descriptive measures of auxiliary variable, including the CDF and coefficient of variation, and tackle the challenge of bandwidth selection using advanced techniques such as plug-in selectors and cross-validation approaches. Simulation studies using datasets on apple production in Turkey and wheat production in Pakistan were conducted to assess the performance of the proposed estimators.

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