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 SANAULLAH2,*, 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
Diserahkan: 11 Januari 2024/Diterima: 11 Jun
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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*Pengarang untuk surat-menyurat; email: chaamirsanaullah@yahoo.com
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