Research

My main research interests are in nonparametric and semi-parametric statistics.

A considerable amount of my recent work is in shape-constrained maximum likelihood estimation. The key idea behind this approach is to strike a balance between parametric methods and purely nonparametric methods by specifying a shape (e.g. convexity) of the function of interest. Unlike kernel smoothing methods, shape-constrained methodology does not require a choice of bandwidth, as it is automatically locally adaptive.

I am also interested in statistical inference for random sets. Random sets are a natural approach to the analysis of shapes, and do not require user-defined landmarks, making them more natural in certain contexts. A closely associated work is the Bayesian approach to principal curves described here, which shows an application to the analysis of SPECT medical imaging data.

My interest in random sets has recently led to research in effective dose estimation in the multivariate setting. When more than one agent is present, the effective dose estimator is essentially a random set. Thus far, my research has focused on developing practical confidence regions in the multivariate setting.

I am also interested in applied and collaborative work. Some recent/current projects include flightpath recovery for migrating songbirds and clustering of the H3N2 flu virus.

Publications:

Trainees are underlined. List of publications split by topic is available here.