We obtain a lower bound for the rate of approximation of bootstrapped empirical processes with Brownian bridges. Our result corresponds to the optimality of the Komlós et al. (1975, 1976, Z. Wahrsch. Verw. Gebiete 32, 111-131; 34, 33-58) approximation of empirical processes.

We study the limiting behavior of the prominent R/S test statistic, aimed at detecting long-range dependence, if instead of long memory a stochastic trend given by cumulative random shocks is present. As the main result we derive the convergence rate of the R/S statistic to its limit.

We develop procedures for testing for changes in the mean of multivariatem-dependent stationary processes. Several test statistics are considered and corresponding limit theorems are derived. These include functional and Darling-Erdos type limit theorems. The tests are shown to be consistent...

Let [beta]n(t) denote the weighted (smooth) bootstrap process of an empirical process. We show that the order of the best Gaussian approximation for [beta]n(t) is n-1/2 log n and we construct a sequence of approximating Brownian bridges achieving this rate. We also obtain an approximation for...

Horvath et al. [2004. Monitoring changes in linear models. J. Statist. Plann. Inference 126, 225-251] developed a family of monitoring procedures to detect a change in the parameters of a linear regression model. These procedures, which are akin to the schemes proposed by Chu et al. [1996....

We propose the quasi-maximum likelihood method to estimate the parameters of an RCA(1) process, i.e. a random coefficient autoregressive time series of order 1. The strong consistency and the asymptotic normality of the estimators are derived under optimal conditions. Copyright 2006 Blackwell...

We propose the quasi-maximum likelihood method to estimate the parameters of an RCA(1) process, i.e. a random coefficient autoregressive time series of order 1. The strong consistency and the asymptotic normality of the estimators are derived under optimal conditions