We show that a fractional Brownian motion with H'E(0,1) can be represented as an explicit transformation of a fractional Brownian motion with index H E(0,1). In particular, when H'=1/2, we obtain a deconvolution formula (or autoregressive representation) for fractional Brownian motion. We work...

This modern and comprehensive guide to long-range dependence and self-similarity starts with rigorous coverage of the basics, then moves on to cover more specialized, up-to-date topics central to current research. These topics concern, but are not limited to, physical models that give rise to...

In a multivariate varying-coefficient model, the response vectors Y are regressed on known functions u(X) of some explanatory variables X and the coefficients in an unknown regression matrix q(Z) depend on another set of explanatory variables Z. We provide statistical tests, called local and...

We focus on the problem of rank estimation in an unknown symmetric matrix based on a symmetric, asymptotically normal estimator of the matrix. The related positive definite limit covariance matrix is assumed to be estimated consistently, and to have either a Kronecker product or an arbitrary...

This work concerns the problem of rank estimation in semidefinite matrices, having either indefinite or semidefinite matrix estimator satisfying a typical asymptotic normality condition. Several rank tests are examined, based on either available rank tests or basic new results. A number of...