In standard parametric classifiers, or classifiers based on nonparametric methods but where there is an opportunity for estimating population densities, the prior probabilities of the respective populations play a key role. However, those probabilities are largely ignored in the construction of...

Lack-of-fit checking for parametric and semiparametric models is essential in reducing misspecification. The efficiency of most existing model-checking methods drops rapidly as the dimension of the covariates increases. We propose to check a model by projecting the fitted residuals along a...

We consider variable selection in the single-index model. We prove that the popular leave-m-out crossvalidation method has different behaviour in the single-index model from that in linear regression models or nonparametric regression models. A new consistent variable selection method, called...

Motivated by two practical problems, we propose a new procedure for estimating a semivarying-coefficient model. Asymptotic properties are established which show that the bias of the parameter estimator is of order h-super-3 when a symmetric kernel is used, where h is the bandwidth, and the...

Distance-based classifiers are generally considered to be effective at discriminating between populations that differ in location. Indeed, nearest-neighbour methods and the support vector machine are frequently used in very high-dimensional problems involving gene expression data, where it is...

If Fourier series are used as the basis for inference in deconvolution problems, the effects of the errors factorise out in a way that is easily exploited empirically. This property is the consequence of elementary addition formulae for sine and cosine functions, and is not readily available...

We suggest a completely empirical approach to the construction of confidence bands for hazard functions, based on smoothing the Nelsen-Aalen estimator. In particular, we introduce a local bandwidth-choice method. Our approach uses empirical information about both the survival rate and the...

We suggest a nonparametric approach to making inference about the structure of distributions in a potentially infinite-dimensional space, for example a function space, and displaying information about that structure. It is suggested that the simplest way of presenting the structure is through...

The objective of this paper is to estimate a bivariate density nonparametrically from a dataset from the joint distribution and datasets from one or both marginal distributions. We develop a copula-based solution, which has potential benefits even when the marginal datasets are empty. For...

Penalised spline regression is a popular new approach to smoothing, but its theoretical properties are not yet well understood. In this paper, mean squared error expressions and consistency results are derived by using a white-noise model representation for the estimator. The effect of the...