Controlling for survey costs when estimating covariances between Pathak estimators in fixed-budget sequential sampling

Szymoniak-Książek Krzysztof () and Gamrot Wojciech ()
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Szymoniak-Książek Krzysztof: Department of Statistics, Econometrics and Mathematics Faculty of Management, University of Economics in Katowice, Katowice, Poland
Gamrot Wojciech: Department of Statistics, Econometrics and Mathematics Faculty of Management, University of Economics in Katowice, Katowice, Poland

Journal of Economics and Management, 2025, vol. 47, issue 1, 211-228

Abstract: Aim/purpose – This work aims to assess stochastic properties of finite population mean estimators under Pathak’s fixed-cost sequential sampling scheme by deriving their covariance and proposing its estimator. This scheme enables strict control over survey-related monetary expenditures when individual data acquisition costs differ and survey budget excesses are unacceptable. It facilitates economically efficient use of available resources. Our work is aimed at extending its applicability. Design/methodology/approach – This paper’s main theoretical result concerning the covariance of Pathak mean value estimators and the unbiasedness of its proposed estimator was derived analytically. A short simulation study supports this. Findings – The proposed estimator for the covariance between Pathak’s estimators of population averages is unbiased under the sequential fixed-cost sampling scheme, which prevents survey budget excesses when the per-unit costs of acquiring information are known in advance but not homogeneous. Research implications/limitations – Our findings facilitate accuracy assessment for complex estimators of population parameters that utilize auxiliary information under restricted-budget sequential sampling and, in particular, for ratio, product, and regression estimators. They are potentially applicable to any quantities of interest that could be expressed in terms of averages, including, among others, unemployment rates, poverty measures, inflation indices, and GDP indicators. Their application is justified if the per-unit costs of acquiring information vary. Originality/value/contribution – Our results allowed us to assess various economic variables’ distribution characteristics while controlling for randomly varying survey costs. This facilitates planning and managing sample surveys in an economically efficient way.

Keywords: Pathak’s estimator; sequential sampling; fixed-cost sampling; sum-quota sampling (search for similar items in EconPapers)
JEL-codes: C15 C83 (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:vrs:jecman:v:47:y:2025:i:1:p:211-228:n:1009

DOI: 10.22367/jem.2025.47.09

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