Suppose that {[xi]j} is a strictly stationary sequence which satisfies the strong mixing condition. Denote by M(k)n the kth largest value of [xi]1,[xi]2,...,[xi]n, and {[upsilon]n(·)} a sequence of normalizing functions for which P[M(1)n[less-than-or-equals, slant][upsilon]n(x)]converges...

Consider a stationary sequence Xj=supiciZj-i,j[set membership, variant]I, where {ci} is a sequence of con {Zi} a sequence of i.i.d. random variables with regularly varying tail probabilities. For suitable normalizing functions [upsilon]1, [upsilon]2,..., the limit form of the two dimensional...

It is shown that if the stationary sequence {Xi} has finite variance and satisfies a certain mixing condition, then the asymptotic distribution of [summation operator]ni=1 Xn is unaffected by the information of whether the summands are in certain "rare" sets. An application of the result shows...

In this paper we introduce a new perspective of linear prediction in the functional data context that predicts a scalar response by observing a functional predictor. This perspective broadens the scope of functional linear prediction currently in the literature, which is exclusively focused on...

A general notion of canonical correlation is developed that extends the classical multivariate concept to include function-valued random elements X and Y. The approach is based on the polar representation of a particular linear operator defined on reproducing kernel Hilbert spaces corresponding...

This paper deals with issues pertaining to estimating the spectral density of a stationary harmonizable [alpha]-stable process, where 0 [alpha] 2. The estimator we consider is obtained by smoothing the periodogram, which has a similar flavor as the usual kernel spectral density estimator for a...

This paper consists of two parts. First, a characterization is obtained for a class of infinitely divisible point processes on . Second, the result is applied to identify the weak limit of the point process Nn with points (j/n, un-1 ([xi]j)), j = 0, ±1, ±2, ..., where {[xi]j} is a...

In this paper the estimation of certain parameters of the extreme order statistics of stationary observations is considered in a general framework. These parameters are resulted from dependence, and hence their inference is substantially different from similar considerations in the i.i.d....

A well-known property of stationary Gaussian processes is that the excursions over high levels ("peaks") have a limiting parabolic shape, each determined by a single random parameter. This means, in particular, that (in the limit) the length of a single excursion above a high level determines...

Characterization theorems are obtained for the possible limits in distribution of a family of stationary random measures {[zeta]T} satisfying a strong mixing condition, with necessary and sufficient conditions for convergence. The application of these results to 'exceedance random measures' is...