In almost all documented applications, the normal-based Lugannani and Rice (1980) formula provides an extremely accurate approximation to tail probabilities. However, it would be wrong to conclude that this formula is always reliable. In the present paper, we consider an example, the first...

Let [gamma] denote the covariance function of a real stationary process on . Define a new function on [-K, K] by [lambda]K(t) = [gamma](t), t [epsilon] [-K, K]. Note that by identifying the end points of the interval, we may interpret [lambda]K as a function on the circle with circumference 2K....

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 consider the non-central distribution of the classical Wilks' lambda statistic for testing the general linear hypothesis in MANOVA. We prove that as the dimension of the observation vector goes to infinity, Wilks' lambda obeys a central limit theorem under simple growth conditions on the...

There has been considerable recent interest in testing for a unit root in autoregressive models, especially in the context of cointegration models in econometrics. The likelihood ratio test for a unit root has non-standard asymptotic behaviour. In particular, when the errors are Gaussian, the...

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...

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...