Title: Variance estimation for non-parametric regression model in systematic sampling under heteroscedastic errors: a simulation study

Authors: Sana Wahid; Javaria Ahmad Khan; Atif Akbar

Addresses: Department of Statistics, Bahuddin Zakariya University, Multan, Pakistan ' Department of Statistics, Bahuddin Zakariya University, Multan, Pakistan ' Department of Statistics, Bahuddin Zakariya University, Multan, Pakistan

Abstract: Systematic sampling is an attractive tool for surveys as it is easily implemented and has an efficient design. In a systematic sample, an important problem is the unavailability of any direct estimator of design variance. A non-parametric model is flexible as it can be applied in different situations with auxiliary variables considered at the population level. Here, different estimators for a non-parametric model are considered for a given population using LPR as an estimation technique for multiple levels of heteroscedastic errors. For comparison, a simulation study is performed for different estimators. This comparison measures the relative bias and mean squared error. It is evident that the local polynomial non-parametric estimator performs well in our proposed situation.

Keywords: non-parametric regression; variance estimation; heteroscedasticity; design-based method; systematic sampling; local polynomial regression.

DOI: 10.1504/IJMMNO.2025.147578

International Journal of Mathematical Modelling and Numerical Optimisation, 2025 Vol.15 No.3, pp.217 - 229

Received: 04 Jan 2025
Accepted: 16 Mar 2025
Published online: 21 Jul 2025 *

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