Bayesian inference for the half-normal and half-t distributions

In this article we consider approaches to Bayesian inference for the half-normal and half-t distributions. We show that a generalized version of the normal-gamma distribution is conjugate to the half-normal likelihood and give the moments of this new distribution. The bias and coverage of the Bayesian posterior mean estimator of the halfnormal location parameter are compared with those of maximum likelihood based estimators. Inference for the half-t distribution is performed using Gibbs sampling and model comparison is carried out using Bayes factors. A real data example is presented which demonstrates the fitting of the half-normal and half-t models

On the efficiency of estimators in truncated height samples

We test the efficiency of estimators proposed for truncated height samples with a new data set of over 23,000 height observations covering nearly all conscripts in Drenthe, a province of the Netherlands, over the period 1826-1860. We find that the `best' estimator, truncated ML, in its unrestricted form overestimates the mean and underestimates the variance. If the variance is set to the population variance, the mean is underestimated. We question the normality assumption that is typically made in this literature. Our `population' is skewed, which might explain the poor performance of the estimators

Diversification Meltdown or the Impact of Fat tails on Conditional Correlation?

A perceived increase in correlation during turbulent market conditions implies a reduction in the benefits arising from portfolio diversification. Unfortunately, it is exactly then that these benefits are most needed. To determine whether diversification truly breaks down, we investigate the robustness of a popular conditional correlation estimator against alternative distributional assumptions. Analytical results show that the apparent meltdown in the benefits from diversification could be a consequence of assuming normally distributed returns. A more realistic assumption - the bivariate Student-t distribution - suggests that constant correlation may be sustained over the full support of the multivariate return distributionConditional correlation, Truncated correlation, Bivariate Student-t correlation.