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...

This paper investigates the rate of convergence of estimating the regression weight function in a functional linear regression model. It is assumed that the predictor as well as the weight function are smooth and periodic in the sense that the derivatives are equal at the boundary points....

Let {[xi]j} be a strictly stationary sequence which satisfies the condition D(un) for some sequence of constants {un}. Write Mn = max([xi]j: 1 [less-than-or-equals, slant] j [less-than-or-equals, slant] n). It is shown that if lim infn -- [infinity]P[Mn [less-than-or-equals, slant] un]0, then...

A distributional mixing condition is introduced for stationary sequences of random vectors to study their extremes. For a sequence satisfying the condition, the following topics which concern the weak limit F of properly normalized partial maxima are studied: (1) To obtain characterizations of...

In the study of intrinsically stationary spatial processes, a new nonparametric variogram estimator is proposed through its spectral representation. The methodology is based on estimation of the variogram's spectrum by solving a regularized inverse problem through quadratic programming. The...

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...