The paper obtains the general form of the cross-covariance function of vector fractional Brownian motions with correlated components having different self-similarity indices.

Some convergence results on the kernel density estimator are proven for a class of linear processes with cyclic effects. In particular, we extend the results of Ho and Hsing (1996), Mielniczuk (1997) and Hall and Hart (1990) to the stationary processes for which the singularities of the spectral...

We construct a two-sample test for comparison of long memory parameters based on ratios of two rescaled variance (V/S) statistics studied in Giraitis et al. [L. Giraitis, R. Leipus, A. Philippe, A test for stationarity versus trends and unit roots for a wide class of dependent errors,...

The problem of the estimation of a multivariate normal mean when the variance is known up to a multiplicative factor is considered under an arbitrary quadratic loss. We introduce shrinkage estimators with differentiable shrinking functions under weak algebraic assumptions. We deduce sufficient...