We extend the standard approach of correlation structure analysis for dimension reduction of high dimensional statistical data. The classical assumption of a linear model for the distribution of a random vector is replaced by the weaker assumption of a model for the copula. For elliptical...

In general, the risk of joint extreme outcomes in financial markets can be expressed as a function of the tail dependence function of a high-dimensional vector after standardizing marginals. Hence, it is of importance to model and estimate tail dependence functions. Even for moderate dimension,...

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...

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...