We obtain limit theorems for sup [alpha]n(t,s)/(t[lambda]s[mu]G(t)L(s)), where [alpha]n is the bivariate uniform empirical process, , , and G, L are slowly varying functions at zero.

We study the asymptotic behaviour of U-statistics type processes which can be used for detecting a changepoint of a random sequence. Invariance principles are proved for these processes.

The general asymptotic order of magnitude is determined for the maximal deviation of the multivariate product-limit estimate from the estimated survival function on Rk. This order depends on the joint behavior of the censoring and censored distributions in a well-defined way. Corresponding to...

We consider some tests to detect a change-point in a multiple linear regression model. The tests are based on the maxima of the weighted cumulative sums processes. The limit distributions may be double exponential or maxima of Gaussian processes depending on the set where the maximum of the...

The quantile process of the product-limit estimator (PL-quantile process) in the random censorship model from the right is studied via strong approximation methods. Some almost sure fluctuation properties of the said process are studied. Sections 3 and 4 contain strong approximations of the...

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...

The functional autoregressive process has become a useful tool in the analysis of functional time series data. It is defined by the equation , in which the observations Xn and errors [epsilon]n are curves, and is an operator. To ensure meaningful inference and prediction based on this model, it...

We discuss some methods to test for possible changes in the parameters of a long-memory sequence. We obtain the limit distributions of the test statistics under the no-change null hypothesis. The consistency of the tests is also investigated.

We develop a theory of asymptotics for Rényi-type weighted empirical and quantile processes and statistics via characterising their possible limiting behaviour in the middle and on the tails. In case of moderate weight functions tail limiting behaviour is found to be Gaussian, while heavily...

Using two definitions of the conditional empirical processes we obtain some approximations for these processes. We also prove the functional law of the iterated logarithm for the conditional processes. Our results say that the asymptotic behavior of the conditional and unconditional empirical...