Motivated by recent work on exploratory projection pursuit, we define the empirical Radon transform. Its precise convergence rate at a fixed centre, uniform over all orientations, and its precise convergence rate uniformly over all centres and all orientations are derived. We show that in the...

We develop mathematical models for high-dimensional binary distributions, and apply them to the study of smoothing methods for sparse binary data. Specifically, we treat the kernel-type estimator developed by Aitchison and Aitken (Biometrika63 (1976), 413-420). Our analysis is of an asymptotic...

In the classical theory of Edgeworth expansion for the sample mean, it is typically assumed that the sampling distribution is either lattice valued or is sufficiently smooth to satisfy Cramér's regularity condition. However, applications of Edgeworth expansions to problems involving the...

Test statistics are proposed for testing equality of two p-variate probability density functions. The statistics are based on the integrated square distance between two kernel-based density estimates and are two-sample versions of the statistic studied by Hall (1984, J. Multivariate Anal. 14...

Two methods are suggested for removing the problem of negativity of high-order kernel density estimators. It is shown that, provided the underlying density has at least moderately light tails, each method has the same asymptotic integrated squared error (ISE) as the original kernel estimator....

Given a sample of n observations from a density [latin small letter f with hook] on d, a natural estimator of [latin small letter f with hook](x) is formed by counting the number of points in some region surrounding x and dividing this count by the d dimensional volume of . This paper presents...

One way of estimating a function from indirect, noisy measurements is to regularise an inverse of its Fourier transformation, using properties of the adjoint of the transform that degraded the function in the first place. It is known that when the function is smooth, this approach can perform...

We suggest a method for reducing variance in nonparametric surface estimation. The technique is applicable to a wide range of inferential problems, including both density estimation and regression, and to a wide variety of estimator types. It is based on estimating the contours of a surface by...

We show that the coverage error of confidence intervals and level error of hypothesis tests for population quantiles constructed using the bootstrap estimate of sample quantile variance is of precise order n-1/2 in both one- and two-sided cases. This contrasts markedly with more classical...

This paper is devoted to tests for uniformity based on sum-functions of m-spacings, where m diverges to infinity as the sample size, n, increases. It is shown that if m diverges at a slower rate than n1/2 then the commonly used sum-function will detect alternatives distant (mn)-1/4 from the...