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

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.