Refinements of first order asymptotic results are reviewed, with a number of Ph.D. projects supervised by van Zwet serving as stepping stones. Berry-Esseen bounds and Edgeworth expansions are discussed for R-, Land U-statistics. After these special classes, the question about a general second order theory for asymptotically normal statistics is addressed. As a final topic, empirical Edgeworth e...

Some limit theorems (including a Berry-Esseen bound) are derived for the number of comparisons taken by the Boyer-Moore algorithm for finding the occurrences of a given pattern in a random Markovian text. Previously, only special variants of this algorithm have been analyzed. We also propose means of computing the limiting constants for the mean and the variance.

Refinements of first order asymptotic results axe reviewed, with a number of Ph.D. projects supervised by van Zwet serving as stepping stones. Berry-Esseen bounds and Edgeworth expansions are discussed for R-, Land [/-statistics. After these special classes, the question about a general second order theory for asymptotically normal statistics is addressed. As a final topic, empirical Edgeworth ...

Let T be a general sampling statistic that can be written as a linear statistic plus an error term. Uniform and non-uniform Berry-Esseen type bounds for T are obtained. The bounds are best possible for many known statistics. Applications to U-statistic, multi-sample U-statistic, L-statistic, random sums, and functions of non-linear statistics are discussed.

We obtain rates of convergence and asymptotic expansions in limit theorems for powers of reciprocals of random variables. Our results improve on recent work of Shapiro [18], who obtained Berry-Esseen bounds of order n~ l/9+c (e > 0). Under weaker conditions than Shapiro imposed we obtain asymptotic expansions whose first term is of order n~ i (logn) 2 .

In various statistical model, such as density estimation and estimation of regression curves or hazard rates, monotonicity constraints can arise naturally. A frequently encountered problem in nonparametric statistics is to estimate a monotone density function f on a compact interval. A known estimator for density function of f under the restriction that f is decreasing, is Grenander estimator, ...

In this paper we describe how the connections between affine forms, zonotopes, and Gaussian distributions help us devise an automated cue integration technique for tracking deformable models. This integration technique is based on the confidence estimates of each cue. We use affine forms to bound these confidences. Affine forms represent bounded intervals, with a well-defined set of arithmetic ...