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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

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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.

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Paper provided by University of Munich, Department of Economics in its series Discussion Papers in Economics with number 51.

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Date of creation: Jul 2003
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Handle: RePEc:lmu:muenec:51

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

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Find related papers by JEL classification:
C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General
C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Statistical Simulation Methods
C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models

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  1. Komlos, John, 2003. "How to (and How Not to) Analyze Deficient Height Samples," Discussion Papers in Economics 56, University of Munich, Department of Economics. [Downloadable!]
  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, March.
  3. Chung, Ching-Fan & Goldberger, Arthur S, 1984. "Proportional Projections in Limited Dependent Variable Models," Econometrica, Econometric Society, vol. 52(2), pages 531-34, March. [Downloadable!] (restricted)
  4. Cole, T. J., 2003. "The secular trend in human physical growth: a biological view," Economics and Human Biology, Elsevier, vol. 1(2), pages 161-168, June. [Downloadable!] (restricted)
  5. John Komlos, . "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.
  6. John Komlos, . "The Secular Trend in the Biological Standard of Living in the United Kingdom, 1730-1860," Articles by John Komlos 19, Department of Economics, University of Munich.
  7. John Komlos, . "On the Nature of the Malthusian Threat in the Eighteenth Century," Articles by John Komlos 6, Department of Economics, University of Munich.
  8. 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. [Downloadable!] (restricted)
  9. John Komlos & Joo Han Kim, . "Estimating Trends in Historical Heights," Articles by John Komlos 25, Department of Economics, University of Munich.
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