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...

The notion of generalized bootstrapping is introduced in Mason and Newton (1992). The study the consistency of generalized bootstrapped means. We extend the validity of the generalized bootstrap to the case of U-statistics and studentized U-statistics. From the proofs it will become clear that...

The critical values for various tests for changes in location model are obtained through the use of permutation tests principle. Theoretical results show that in the limit these new "permutation tests" behave in the same way as the "classical tests" stemming from both maximum likelihood and...

In the present paper there is proposed a rank statistic for multivariate testing of randomness conceriing some marginal distributions. The asymptotic distribution of this statistic under hypothesis and "near" alternatives is treated.

An estimator of the change point in the linear model is proposed and its asymptotic properties (the rate of consistency and the limit distribution) are derived. This estimator is then used to construct estimators for the magnitude of the change of the regression parameters and of the scale....

The present paper contains assertions on asymptotic distributions of statistics used for the nonparametric multivariate testing symmetry. The results are proved under the hypothesis of symmetry H1, the near alternative and the general alternative. The proofs of the main theorems (Theorems 2.3,...

The rates of convergence of the distribution function of quadratic rank statistics to the X2-distribution under hypothesis and near alternatives are investigated. The considered quadratic rank statistics are used for testing the multivariate hypothesis of randomness. The method suggested by...

Consistent procedures are constructed for testing independence between the regressor and the error in non-parametric regression models. The tests are based on the Fourier formulation of independence, and utilize the joint and the marginal empirical characteristic functions of the regressor and...