Michael Stewart (USyd, School of Mathematics and Statistics)
Title: Estimating non-smooth scale functionals of random effect distributions
We report on recent progress in ongoing work, jointly with Professor Alan Welsh of ANU, on inference concerning scale parameters of latent distributions in random effect models. An overarching motivation is robustness which in turn motivates the following two aims: (a) that robust, possibly non-smooth scale functionals, like interquartile range or median absolute deviation (from the median) might be of interest; (b) that we guard as much as possible against model misspecification. This leads us to consider bringing the substantial literature on semiparametric theory to bear on the problem. Semiparametric theory leads to optimal inference for Euclidean parameters in the presence of infinite-dimensional nuisance parameters, i.e. nuisance functions. We can thus regard the shape of the latent distribution, as well as the densities of residuals as nuisance functions and try to develop methods which attain good performance regardless of the value of the nuisance functions. The talk will give an overview of semiparametric methods in the case of a standard location/scale problem and in particular point out models where so-called efficient score functions may be identified which do not depend on nuisance functions. We then detail our efforts at transferring such properties to the random effects model. We point out connections with recently developed semiparametric methods in missing data models and also the limitations of such methods in our setting. Unsurprisingly, since we are dealing with latent distributions, Bayesian theory also has some relevance to our problem and we also point out ways we have tried to exploit this. Finally we present and discuss the results of some simulations which indicate that our methods may indeed offer some improvement over existing “naïve” methods.