We describe a unified approach to the construction of confidence bands in nonparametric density estimation and regression. Our techniques are based on interpolation formulae in numerical differentiation, and our arguments generate a variety of bands depending on the assumptions one is prepared...

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...

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...

Let Y be an absolutely continuous random variable and W a nonnegative variable independent of Y. It is to be expected that when W is close to 1 in some sense, the distribution of the scale mixture YW will be close to Y. This notion has been investigated by a number of workers, who have provided...

Three limit theorems describing asymptotic distribution of vacancy in general multivariate coverage problems are proved, in which n k-dimensional spheres are distributed within a k-dimensional unit cube according to a density f. The first result (a central limit theorem) describes the case where...

A recent paper by Mack and Rosenblatt (J. Multivar. Anal. 9 (1979), 1-15) has shown that near neighbour estimators of a density may perform more poorly than other kernel-type estimators, particularly for x values in the tail of a distribution. In order to overcome the difficulties discovered by...

We point out that inliers adversely affect performance of the spatial median and its generalization due to Gentleman. They are most deleterious in the case of the median itself, and in the important setting of two dimensions. There, the second term in a stochastic expansion of the median has a...