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Improvements in Maximum Likelihood Estimators of Truncated Normal Samples with Prior Knowledge of σ

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  • A'Hearn, Brian
  • Komlos, John

Abstract

Researchers analyzing historical data on human stature have long sought an estimator that performs well in truncated-normal samples. This paper reviews that search, focusing on two currently widespread procedures: truncated least squares (TLS) and truncated maximum likelihood (TML). The first suffers from bias. The second suffers in practical application from excessive variability. A simple procedure is developed to convert TLS truncated means into estimates of the underlying population means, assuming the contemporary population standard deviation. This procedure is shown to be equivalent to restricted TML estimation. Simulation methods are used to establish the mean squared error performance characteristics of the restricted and unconstrained TML estimators in relation to several population and sample parameters. The results provide general insight into the bias-precision tradeoff in restricted estimation and a specific practical guide to optimal estimator choice for researchers in anthropometrics.

Suggested Citation

  • A'Hearn, Brian & Komlos, John, 2003. "Improvements in Maximum Likelihood Estimators of Truncated Normal Samples with Prior Knowledge of σ," Discussion Papers in Economics 51, University of Munich, Department of Economics.
    • Handle: RePEc:lmu:muenec:51
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    File URL: https://epub.ub.uni-muenchen.de/51/1/bias-precision.pdf
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    References listed on IDEAS

    as
    1. John Komlos, 1993. "The secular trend in the biological standard of living in the United Kingdom, 1730-1860," Economic History Review, Economic History Society, vol. 46(1), pages 115-144, February.
    2. John Komlos, 1989. "Nutrition and Economic Development in the Eighteenth-Century Habsburg Monarchy: An Anthropometric History," Books by John Komlos, Department of Economics, University of Munich, number 2, June.
    3. Ruud, Paul A., 2000. "An Introduction to Classical Econometric Theory," OUP Catalogue, Oxford University Press, number 9780195111644.
    4. Chung, Ching-Fan & Goldberger, Arthur S, 1984. "Proportional Projections in Limited Dependent Variable Models," Econometrica, Econometric Society, vol. 52(2), pages 531-534, March.
    5. Cole, T. J., 2003. "The secular trend in human physical growth: a biological view," Economics & Human Biology, Elsevier, vol. 1(2), pages 161-168, June.
    6. John Komlos, "undated". "Stature and Nutrition in the Habsburg Monarchy: The Standard of Living and Economic Development," Articles by John Komlos 36, Department of Economics, University of Munich.
    7. Komlos, John, 2003. "How to (and How Not to) Analyze Deficient Height Samples," Discussion Papers in Economics 56, University of Munich, Department of Economics.
    8. John Komlos, 1999. "On the nature of the Malthusian threat in the eighteenth century," Economic History Review, Economic History Society, vol. 52(4), pages 730-748, November.
    9. Kenneth Y. Chay & James L. Powell, 2001. "Semiparametric Censored Regression Models," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 29-42, Fall.
    10. John Komlos & Joo Han Kim, "undated". "Estimating Trends in Historical Heights," Articles by John Komlos 25, Department of Economics, University of Munich.
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    1. repec:dgr:rugccs:200408 is not listed on IDEAS
    2. Zehetmayer, Matthias, 2010. "An Anthropometric History of the Postbellum US, 1847-1894," Munich Dissertations in Economics 12321, University of Munich, Department of Economics.
    3. Jacobs, Jan & Katzur, Tomek & Tassenaar, Vincent, 2004. "On the efficiency of estimators in truncated height samples," CCSO Working Papers 200408, University of Groningen, CCSO Centre for Economic Research.
    4. Jacobs, Jan & Katzur, Tomek & Tassenaar, Vincent, 2008. "On estimators for truncated height samples," Economics & Human Biology, Elsevier, vol. 6(1), pages 43-56, March.
    5. Dobado González, Rafael & García Montero, Héctor, 2010. "Colonial Origins of Inequality in Hispanic America? Some Reflections Based on New Empirical Evidence," Revista de Historia Económica / Journal of Iberian and Latin American Economic History, Cambridge University Press, vol. 28(2), pages 253-277, September.

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    More about this item

    Keywords

    truncated least squares; truncated maximum likelihood (TML); simulation methods; bias-precision trade-off; anthropometrics;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models

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