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. Ruud, Paul A., 2000. "An Introduction to Classical Econometric Theory," OUP Catalogue, Oxford University Press, number 9780195111644.
    3. Komlos, John & Baur, Marieluise, 2004. "From the tallest to (one of) the fattest: the enigmatic fate of the American population in the 20th century," Economics & Human Biology, Elsevier, vol. 2(1), pages 57-74, March.
    4. 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.
    5. John Komlos & Joo Han Kim, "undated". "Estimating Trends in Historical Heights," Articles by John Komlos 25, Department of Economics, University of Munich.
    6. 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.
    7. Chung, Ching-Fan & Goldberger, Arthur S, 1984. "Proportional Projections in Limited Dependent Variable Models," Econometrica, Econometric Society, vol. 52(2), pages 531-534, March.
    8. 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.
    9. Komlos, John, 2003. "How to (and How Not to) Analyze Deficient Height Samples," Discussion Papers in Economics 56, University of Munich, Department of Economics.
    10. 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.
    11. 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. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. A'Hearn, Brian, 2004. "A restricted maximum likelihood estimator for truncated height samples," Economics & Human Biology, Elsevier, vol. 2(1), pages 5-19, March.
    2. Komlos, John, 2003. "How to (and How Not to) Analyze Deficient Height Samples," Discussion Papers in Economics 56, University of Munich, Department of Economics.
    3. Komlos, John & Cinnirella, Francesco, 2005. "European Heights in the Early 18th Century," Discussion Papers in Economics 572, University of Munich, Department of Economics.
    4. John Komlos & Leonard Carlson, 2014. "The anthropometric history of Native Americans, C.1820–1890," Research in Economic History, in: Research in Economic History, volume 30, pages 135-161, Emerald Group Publishing Limited.
    5. Schoch, Tobias & Staub, Kaspar & Pfister, Christian, 2012. "Social inequality and the biological standard of living: An anthropometric analysis of Swiss conscription data, 1875–1950," Economics & Human Biology, Elsevier, vol. 10(2), pages 154-173.
    6. Galofré-Vilà, Gregori, 2018. "Growth and maturity: A quantitative systematic review and network analysis in anthropometric history," Economics & Human Biology, Elsevier, vol. 28(C), pages 107-118.
    7. Cranfield, John & Inwood, Kris, 2007. "The great transformation: A long-run perspective on physical well-being in Canada," Economics & Human Biology, Elsevier, vol. 5(2), pages 204-228, July.
    8. John Komlos, "undated". "On the Biological Standard of Living of Eighteenth-Century Americans: Taller, Richer, Healthier," Articles by John Komlos 3, Department of Economics, University of Munich.
    9. Kopczyński, Michał, 2019. "Between the Great War and the Great Depression: preliminary observations on the ‘missing link’ in the history of human stature in Poland," Economics & Human Biology, Elsevier, vol. 34(C), pages 162-168.
    10. Hiermeyer, Martin, 2010. "The height and BMI values of West Point cadets after the Civil War," Economics & Human Biology, Elsevier, vol. 8(1), pages 127-133, March.
    11. Staub, Kaspar & Rühli, Frank J. & Bogin, Barry & Woitek, Ulrich & Pfister, Christian, 2011. "Edouard Mallet's early and almost forgotten study of the average height of Genevan conscripts in 1835," Economics & Human Biology, Elsevier, vol. 9(4), pages 438-442.
    12. Leonardo Monteiro Monastério & Mateus Signorini, 2008. "As condições de vida dos gaúchos entre 1889-1920: uma análise antropométrica," Anais do XXXVI Encontro Nacional de Economia [Proceedings of the 36th Brazilian Economics Meeting] 200807202137560, ANPEC - Associação Nacional dos Centros de Pós-Graduação em Economia [Brazilian Association of Graduate Programs in Economics].
    13. de Beer, Hans, 2004. "Observations on the history of Dutch physical stature from the late-Middle Ages to the present," Economics & Human Biology, Elsevier, vol. 2(1), pages 45-55, March.
    14. Roderick Floud & Bernard Harris, 1997. "Health, Height, and Welfare: Britain, 1700-1980," NBER Chapters, in: Health and Welfare during Industrialization, pages 91-126, National Bureau of Economic Research, Inc.
    15. Bassino, Jean-Pascal, 2006. "Inequality in Japan (1892-1941): Physical stature, income, and health," Economics & Human Biology, Elsevier, vol. 4(1), pages 62-88, January.
    16. Ramon Ramon-Muñoz & Josep-Maria Ramon-Muñoz, 2015. "Height and Industrialisation in a City in Catalonia during the Nineteenth Century," UB School of Economics Working Papers 2015/334, University of Barcelona School of Economics.
    17. Komlos, John, 2012. "A Three-Decade “Kuhnian” History of the Antebellum Puzzle: Explaining the shrinking of the US population at the onset of modern economic growth," Discussion Papers in Economics 12758, University of Munich, Department of Economics.
    18. Jacobs, Jan & Tassenaar, Vincent, 2004. "Height, income, and nutrition in the Netherlands: the second half of the 19th century," Economics & Human Biology, Elsevier, vol. 2(2), pages 181-195, June.
    19. Scott A. Carson, 2010. "Nineteenth Century US African-American and White Female Statures: Insight from US Prison Records," CESifo Working Paper Series 3169, CESifo.
    20. Carson, Scott Alan, 2011. "Height of female Americans in the 19th century and the antebellum puzzle," Economics & Human Biology, Elsevier, vol. 9(2), pages 157-164, March.

    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

    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.

    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 bibliographic 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.

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

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.