On estimators for truncated height samples

Statistical inference from truncated height data is often based on distributional assumptions. In this paper we analyze a data set of over 23,000 conscript height observations, covering nearly all conscripts in Drenthe, a province of the Netherlands, over the period 1826-1860. The data do not satisfy the normality assumption. We demonstrate that the ML estimators of the mean proposed for normally distributed data do not yield satisfactory results. We propose a new estimator that exploits the relationship between the conditional mean of the observations above the minimum height requirement and the conditional mean and proportion of conscripts below the minimum height requirement.