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Bootstrap for nonlinear statistics like U-statistics of dependent data has been studied by several authors. This is typically done by producing a bootstrap version of the sample and plugging it into the statistic. We suggest an alternative approach of getting a bootstrap version of U-statistics, which can be described as a compromise between bootstrap and subsampling. We will show the consistency of the new method and compare its finite sample properties in a simulation study.
In this paper we analyze different ways of performing principal component analysis throughout three different approaches: robust covariance and correlation matrix estimation, projection pursuit approach and non-parametric maximum entropy algorithm. T
This paper derives central limit and bootstrap theorems for probabilities that sums of centered high-dimensional random vectors hit hyperrectangles and sparsely convex sets. Specifically, we derive Gaussian and bootstrap approximations for probabilit
In 1975 John Tukey proposed a multivariate median which is the deepest point in a given data cloud in R^d. Later, in measuring the depth of an arbitrary point z with respect to the data, David Donoho and Miriam Gasko considered hyperplanes through z
The purpose of this note is to provide an approximation for the generalized bootstrapped empirical process achieving the rate in Kolmos et al. (1975). The proof is based on much the same arguments as in Horvath et al. (2000). As a consequence, we est
We introduce a new sufficient statistic for the population parameter vector by allowing for the sampling design to first be selected at random amongst a set of candidate sampling designs. In contrast to the traditional approach in survey sampling, we