Estimating Historical Heights

Abstract Historical samples of military, naval, and merchant marine heights suffer from undercounts of short people, undercounts highly irregular compared to the truncated distributions for which standard methods are available. Our knowledge is too imprecise for parametric models of the undercount process but it suffices for intuitive description of the deviations from normality with which estimators should cope. Two new estimators are developed. The first adapts maximum likelihood for truncated normals to height histograms with gradual lower-tail shortfall. The second exploits bends in quantile-quantile plots. Standard error estimates based on Efron's bootstrap appear reliable. The estimators show average heights from British Royal Marine samples much shorter than their American opponents in the Revolutionary War and reveal a statistically significant increase by the 1820's in the British heights.

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