We prove the weak convergence of the empirical process of a(n) close pairs. The limit process is always Gaussian but its form depends on how fast the sequence a(n) goes to zero.

We consider a sequential test procedure which detects possible changes in the mean of observations satisfying a weak invariance principle. Our test statistic is based on weighted CUSUMs of the underlying random variables. In this paper, we study the asymptotic behaviour of the delay time if a...

We consider a multiple regression model in which the explanatory variables are specified by time series. To sequentially test for the stability of the regression parameters in time, we introduce a detector which is based on the first excess time of a CUSUM-type statistic over a suitably...

We propose a nonparametric estimator for the rate of spread of an introduced population. We prove that the limit distribution of the estimator is normal or stable, depending on the behavior of the moment generating function. We show that resampling methods can also be used to approximate the...

We propose a test for a change in the parameters of a GARCH(p,q) model. The test is based on approximate likelihood scores and does not require the observations to have finite variance. We show that the test has asymptotically correct size under weak assumptions on model errors.

We find necessary and sufficient conditions for the almost sure finiteness of weighted integrals of stable processes with parameters [alpha] = 1 and [beta] [not equal to] 0.

This note represents a probability inequality for an approximation of Abel sums of independent, identically distributed random variables. This approximation implies a rate for the Prohorov-Lévy distance between Abel sums and their limit process.

The paper develops a comprehensive asymptotic theory for the estimation of a change-point in the mean function of functional observations. We consider both the case of a constant change size, and the case of a change whose size approaches zero, as the sample size tends to infinity. We show how...