Sains Malaysiana 53(7)(2024): 1693-1702

http://doi.org/10.17576/jsm-2024-5307-16

Enhancing Precision in Population Variance Vector Estimation: A Two-Phase Sampling Approach with Multi-Auxiliary Information

(Meningkatkan Ketepatan dalam Anggaran Vektor Varians Populasi: Pendekatan Persampelan Dua Fasa dengan Maklumat Berbilang Bantu)

AMBER ASGHAR¹, AAMIR SANAULLAH^2,*, MUHAMMAD HANIF³ & LAILA A. AL-ESSA⁴

  ¹Department of Statistics, Faculty of Science and Technology, Virtual University of Pakistan, Lahore, Pakistan

²Department of Statistics, COMSATS University Islamabad Lahore Campus, Pakistan

³Department of Statistics, National College of Business Administration & Economics, Lahore, Pakistan

⁴Department of Mathematical Sciences, College of Sciences, Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia

Received: 11 January 2024/Accepted: 11 June 2024

Abstract

To enhance precision in estimating unknown population parameters, an auxiliary variable is often used. However, in scenarios where required information on an auxiliary variable is partially or fully unavailable, two-phase sampling is commonly employed. The challenge of estimating the variance vector using multi-auxiliary variables is a less explored area in current literature. This paper addresses the estimation of vector of unknown population variances for multiple study variables by using an estimated vector of variances derived from multi-auxiliary information. This approach is particularly relevant when population variances for the multi-auxiliary variables are not known prior to the survey. The paper introduces a generalized variance and a vector of biases for the proposed multivariate estimator. Special cases of the proposed multivariate variance estimator are provided, accompanied by expressions for mean square errors. Theoretical mathematical conditions are discussed to guide the preference for the proposed estimator. Through the analysis of real-world application-based data, the applicability and efficiency of the proposed multivariate variance estimator are demonstrated, outperforming modified versions of multivariate variance estimators. Additionally, a simulation study validates the superior performance of the proposed estimator compared to its modified estimators.

Keywords: Generalized variance; multivariate estimator; regression-cum-exponential estimator; two-phase sampling; variance vector estimator

Abstrak

Untuk meningkatkan ketepatan dalam menganggar parameter populasi yang tidak diketahui, pemboleh ubah bantuan sering digunakan. Walau bagaimanapun, dalam senario yang mana maklumat yang diperlukan tentang pemboleh ubah bantuan sebahagian atau sepenuhnya tidak tersedia, pensampelan dua fasa biasanya digunakan. Cabaran untuk menganggar vektor varians menggunakan pemboleh ubah berbilang bantu adalah bidang yang kurang diterokai dalam kepustakaan semasa. Kertas ini menangani anggaran vektor varians populasi yang tidak diketahui untuk pelbagai pemboleh ubah kajian dengan menggunakan anggaran vektor varians yang diperoleh daripada maklumat berbilang bantu. Pendekatan ini amat relevan apabila varians populasi untuk pemboleh ubah berbilang bantu tidak diketahui sebelum tinjauan. Makalah ini memperkenalkan varians umum dan vektor bias untuk penganggar multivariat yang dicadangkan. Kes khas penganggar varians multivariat yang dicadangkan disediakan, disertakan dengan pengekspresan untuk ralat kuasa dua min. Keadaan matematik teori dibincangkan untuk membimbing keutamaan bagi penganggar yang dicadangkan. Melalui analisis data berasaskan aplikasi dunia sebenar, kebolehgunaan dan kecekapan penganggar varians multivariat yang dicadangkan ditunjukkan, mengatasi versi pengubahsuaian penganggar varians multivariat. Selain itu, kajian simulasi mengesahkan prestasi unggul penganggar yang dicadangkan berbanding penganggarnya yang diubah suai.

Kata kunci: Penganggar multivariat; penganggar regresi merangkap eksponen; penganggar vektor varians; pensampelan dua fasa; varians umum

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*Corresponding author; email: chaamirsanaullah@yahoo.com