IDEAS home Printed from https://ideas.repec.org/p/lmu/muenec/51.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://epub.ub.uni-muenchen.de/51/1/bias-precision.pdf
    Download Restriction: no

    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. 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.
    3. John Komlos & Joo Han Kim, "undated". "Estimating Trends in Historical Heights," Articles by John Komlos 25, Department of Economics, University of Munich.
    4. 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.
    5. Chung, Ching-Fan & Goldberger, Arthur S, 1984. "Proportional Projections in Limited Dependent Variable Models," Econometrica, Econometric Society, vol. 52(2), pages 531-534, March.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Zehetmayer, Matthias, 2010. "An Anthropometric History of the Postbellum US, 1847-1894," Munich Dissertations in Economics 12321, University of Munich, Department of Economics.
    2. Jacobs, Jan & Katzur, Tomek & Tassenaar, Vincent, 2008. "On estimators for truncated height samples," Economics & Human Biology, Elsevier, vol. 6(1), pages 43-56, March.
    3. 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, Cambridge University Press, vol. 28(02), pages 253-277, September.

    More about this item

    Keywords

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

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:lmu:muenec:51. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Tamilla Benkelberg). General contact details of provider: http://edirc.repec.org/data/vfmunde.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.