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Modern Approaches to Statistical Estimation of Measurements in the Location Model and Regression

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Handbook of Metrology and Applications

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Abstract

Metrology as the science about measurement is highly intertwined with statistical point estimation. Evaluating and controling uncertainty of measurements and analyzing them by means of exploratory data analysis (EDA) or predictive data mining requires to exploit advanced tools of statistical estimation. The main focus of the chapter is devoted to nonstandard approaches to the analysis of measurements in two fundamental models, namely, the location model and linear regression. Robust regression methods, which are resistant to the presence of outlying (anomalous) measurements, are discussed here. An illustration of their performance over a real dataset related to thyroid disease and a Monte Carlo simulation reveal here the least weighted squares estimator, which has remained quite neglected so far, outperforms much more renowned robust regression estimators in terms of the variability. Further, Bayesian estimation in the location model is revealed here to have the ability to incorporate previous measurements in a very intuitive way. Finally, the chapter gives a warning that linear regression performed on data contaminated by measurement errors yields biased estimates and requires specific estimation tools for the so-called measurement error model.

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Acknowledgments

The work of J. Kalina was supported by the project GA22-02067S (Approximate Neurocomputing) of the Czech Science Foundation. The authors would like to thank an anomymous reviewer for valuable suggestions.

Author information

Authors and Affiliations

  1. Institute of Computer Science, The Czech Academy of Sciences, Prague, Czech Republic

    Jan Kalina & Petra Vidnerová

  2. Institute of Information Theory and Automation, The Czech Academy of Sciences, Prague, Czech Republic

    Lubomír Soukup

Authors
  1. Jan Kalina
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  2. Petra Vidnerová
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  3. Lubomír Soukup
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Corresponding author

Correspondence to Jan Kalina .

Editor information

Editors and Affiliations

  1. Bhabha Atomic Research Centre, Mumbai, Maharashtra, India

    Dinesh K. Aswal

  2. Physico-Mechanical Metrology, CSIR - National Physical Laboratory, New Delhi, Delhi, India

    Sanjay Yadav

  3. National Metrology Institute of Japan, National Institute of Advanced Industria, Ibaraki, Japan

    Toshiyuki Takatsuji

  4. National Institute of Standards and Tech, GAITHERSBURG, MD, USA

    Prem Rachakonda

  5. Mechanical Engineering Department, National Institute of Technology, Delhi, India

    Harish Kumar

Section Editor information

  1. CSIR-National Physical Laboratory, New Delhi, India

    Naveen Garg

  2. Department of Mechanical Engineering, University of South Africa (Unisa), Pretoria, South Africa

    Vishal Ramnath

  3. HFPL, Bangalore, India

    B. K. Das

  4. Physico-Mechanical Metrology Division, CSIR-National Physical Laboratory, New Delhi, Delhi, India

    Sanjay Yadav

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Kalina, J., Vidnerová, P., Soukup, L. (2022). Modern Approaches to Statistical Estimation of Measurements in the Location Model and Regression. In: Aswal, D.K., Yadav, S., Takatsuji, T., Rachakonda, P., Kumar, H. (eds) Handbook of Metrology and Applications. Springer, Singapore. https://doi.org/10.1007/978-981-19-1550-5_125-1

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  • DOI: https://doi.org/10.1007/978-981-19-1550-5_125-1

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  • Print ISBN: 978-981-19-1550-5

  • Online ISBN: 978-981-19-1550-5

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