Functional principal components (FPC’s) provide the most important and most extensively used tool for dimension reduction and inference for functional data. The selection of the number, d, of the FPC’s to be used in a specific procedure has attracted a fair amount of attention, and a number...

We wish to test the null hypothesis that a collection of functional observations are independent and identically distributed. Our procedure is based on the sum of the L2 norms of the empirical correlation functions. The limit distribution of the proposed test statistic is established under the...

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...

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 obtain limit theorems for likelihood ratio and cumulative sums tests. In the case of the likelihood ratio the centralising and normalising sequences go to infinity and the limit is the Gumbel (double exponential) distribution. The first and the last few observations determine the limit, which...

We deal with quantile processes based on intermediate order statistics. Using an approximation of the uniform quantile process in weighted metrics, we prove weak convergence of weighted and nonweighted intermediate quantile processes.

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.