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

Author

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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)

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.

Suggested Citation

  • Szymoniak-Książek Krzysztof & Gamrot Wojciech, 2025. "Controlling for survey costs when estimating covariances between Pathak estimators in fixed-budget sequential sampling," Journal of Economics and Management, Sciendo, vol. 47(1), pages 211-228.
  • Handle: 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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    References listed on IDEAS

    as
    1. James H. Stock & Mark W. Watson, 2016. "Core Inflation and Trend Inflation," The Review of Economics and Statistics, MIT Press, vol. 98(4), pages 770-784, October.
    2. Wojciech Gamrot, 2012. "Estimation of finite population kurtosis under two-phase sampling for nonresponse," Statistical Papers, Springer, vol. 53(4), pages 887-894, November.
    3. Roberto Benedetti & Federica Piersimoni & Paolo Postiglione, 2015. "Spatial Sampling Designs," Advances in Spatial Science, in: Sampling Spatial Units for Agricultural Surveys, edition 127, chapter 0, pages 149-196, Springer.
    4. N. Mukhopadhyay & T. Solanky, 1997. "Estimation after sequential selection and ranking," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 45(1), pages 95-106, January.
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    More about this item

    Keywords

    Pathak’s estimator; sequential sampling; fixed-cost sampling; sum-quota sampling;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C83 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Survey Methods; Sampling Methods

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