Measurement Techniques

, Volume 42, Issue 11, pp 1009–1016 | Cite as

A central limit theorem for linear estimators of measurement results

  • E. V. Eremin
General Problems of Metrology and Measurement Technology


The central limit theorem for the first weighted moments of a distribution of independent random variables is proved. General conditions for the limiting convergence of the sequence of sampling estimators of the weighted mean to the center of the normal distribution are established.


Confidence Limit Central Limit Theorem Weight Coefficient Standard Normal Distribution Linear Estimator 


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  1. 1.
    G. D. Burdun and B. N. Markov,Foundations of Metrology [in Russian], Moscow, Izdatel'stvo Standartov (1985).Google Scholar
  2. 2.
    N. I. Tyurin,Introduction to Metrology [in Russian], Moscow, Izdatel'stro Standartov (1985).Google Scholar
  3. 3.
    M. N. Selivanov, A. É. Fridman, and Zh. F. Kudryashova,The Quality of Measurements: Metrological Handbook [in Russian], Lenizdat, Leningrad (1987).Google Scholar
  4. 4.
    V. A. Granovskii and T. N. Siraya,Methods of Processing Experimental Data of Measurements [in Russian], Énergoatomizdat, Leningrad Branch, Leningrad (1990).Google Scholar
  5. 5.
    S. A. Aivazyan, I. S. Enyukov, and L. D. Meshalkin,Applied Statistics: Foundations of Modelling and Initial Data Processing, Handbook Edition [in Russian], Finansy i Statistika, Moscow (1983).Google Scholar
  6. 6.
    H. Cramér,Mathematical Methods of Statistics, Princeton University Press, Princeton, N. J. (1946).MATHGoogle Scholar
  7. 7.
    V. N. Tutubalin,Probability Theory and Random Processes [in Russian], Moscow State University Press, Moscow (1992)Google Scholar
  8. 8.
    E. V. Eremin,Izmer. Tekh., No. 7, 14 (1999).Google Scholar
  9. 9.
    G. M. Fikhtengol'tz,Course in Differential and Integral Calculus [in Russian], Vol. 1, Nauka, Moscow (1969).Google Scholar
  10. 10.
    J. Pollard,Handbook of Computational Methods of Statistics, [Russian translation], Finansy i Statistika, Moscow (1982). RussianGoogle Scholar

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© Kluwer Academic/Plenum Publishers 1999

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  • E. V. Eremin

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