The Fisher--Bingham distribution is obtained when a multivariate normal random vector is conditioned to have unit length. Its normalising constant can be expressed as an elementary function multiplied by the density, evaluated at 1, of a linear combination of independent noncentral...

Empirical Bayes approaches to the shrinkage of empirical wavelet coefficients have generated considerable interest in recent years. Much of the work to date has focussed on shrinkage of individual wavelet coefficients in isolation. In this paper we propose an empirical Bayes approach to...

We consider empirical likelihood for the mean similarity shape of objects in two dimensions described by labelled landmarks. The restriction to two dimensions permits the representation of preshapes as complex unit vectors. We focus on the use of empirical likelihood techniques for the...

Working within the framework of a multi-dimensional scaling approach to shape analysis, we develop bootstrap methods for inference about mean reflection shape and size-and-shape based on labelled landmark data. The approach is developed in general dimensions though we focus on the...

In an earlier paper Kume & Wood (2005) showed how the normalizing constant of the Fisher--Bingham distribution on a sphere can be approximated with high accuracy using a univariate saddlepoint density approximation. In this sequel, we extend the approach to a more general setting and derive...

We propose an alternative to Kendall's shape space for reflection shapes of configurations in <inline-formula><inline-graphic xlink:href="asn050ilm1.gif" xmlns:xlink="http://www.w3.org/1999/xlink"/></inline-formula> with k labelled vertices, where reflection shape consists of all the geometric information that is invariant under compositions of similarity and reflection transformations. The proposed approach...