Let Tn be a U-statistic and Sn its projection (in the sense of Hájek). Limit theory for U-statistics is usually considered in two disjoint cases, termed degenerate and nondegenerate. The traditional method is to treat the cases separately, using different techniques in each to obtain a...

Series expansions of moments of order statistics are obtained from expansions of the inverse of the distribution function. They are valid for certain types of distributions with regularly varying tails. We show that the expansions converge quickly when the sample size is moderate to large, and...

In a previous paper in this Journal, Heyde and Leslie [6] examined moment measures of the distance of a mixture from its parent distribution. They confined their attention to the case where the parent distribution is either normal or exponential, and related the moment measures to the more...

Plateau honing is a way of enhancing the lubricant retention qualities of interfacing surfaces which are in relative motion. Surfaces prepared in this way enjoy two levels of roughness, which broadly correspond to a sequence of smooth plateaus at which they touch, and a series of rough crevices...

The effect of dependent errors in fixed-design, nonparametric regression is investigated. It is shown that convergence rates for a regression mean estimator under the assumption of independent errors are maintained in the presence of stationary dependent errors, if and only if [Sigma] r(j) ...

Stochastic measures of the distance between a density f and its estimate fn have been used to compare the accuracy of density estimators in Monte Carlo trials. The practice in the past has been to select a measure largely on the basis of its ease of computation, using only heuristic arguments to...

The random distribution of line segments on a circle is used in several applications to model a physical surface being impinged upon at random by foreign bodies. In this context, the hypothesis of uniformity suggests that the bodies come from all directions with equal probabilities, and have no...

The possibility of resampling (bootstrapping) a spatial pattern is investigated. It is suggested that resampling provides a unified approach to consistemt inference in a wide range of coverage problems. Nevertheless, resampling distorts some of the interactions in the problem, and so introduces...

We study a generalised version of the logistic map of the unit interval in which the point is taken to . Here, is a parameter of the map, which has received attention only when and . We obtain the invariant density when , and derive properties of invariant distributions in all other cases. These...

Let X denote the mean of a consecutive sequence of length n from an autoregression or moving average process. Suppose the covariance function of the process is regularly varying with exponent -[alpha], where [alpha] [greater-or-equal, slanted] 0. We show that the rate of convergence in a central...