A number of different approaches to study multivariate extremes have been developed. Arguably the most useful and flexible is the theory for the distribution of a vector variable given that one of its components is large. We build on the conditional approach of Heffernan and Tawn (2004) [13]...

We consider maximum likelihood estimation of a particular noninvertible ARMA model with autoregressive conditionally heteroskedastic (ARCH) errors. The model can be seen as an extension to the so-called all-pass models in that it allows for autocorrelation and for more flexible forms of...

The Gaussian sequence model can be obtained from the high-dimensional regression model through principal component analysis. It is shown that the Gaussian sequence model is equivalent to the original high-dimensional regression model in terms of prediction. Under a sparsity condition, we...

We consider the moment space MnK corresponding to p×p complex matrix measures defined on K (K=[0,1] or K=T). We endow this set with the uniform distribution. We are mainly interested in large deviation principles (LDPs) when n→∞. First we fix an integer k and study the vector of the first k...

The constraint that a covariance matrix must be positive definite presents difficulties for modeling its structure. Pourahmadi (1999, 2000) [18,19] proposed a parameterization of the covariance matrix for univariate longitudinal data in which the parameters are unconstrained, which is based on...

Given a random vector X, we address the question of linear separability of X, that is, the task of finding a linear operator W such that we have (S1,…,SM)=(WX) with statistically independent random vectors Si. As this requirement alone is already fulfilled trivially by X being independent of...

In this paper, we establish some results for the increasing convex comparisons of generalized order statistics. First, we prove that if the minimum of two sets of generalized order statistics are ordered in the increasing convex order, then the remaining generalized order statistics are also...

In nonparametric classification and regression problems, regularized kernel methods, in particular support vector machines, attract much attention in theoretical and in applied statistics. In an abstract sense, regularized kernel methods (simply called SVMs here) can be seen as regularized...

We consider a difference based ridge regression estimator and a Liu type estimator of the regression parameters in the partial linear semiparametric regression model, y=Xβ+f+ε. Both estimators are analyzed and compared in the sense of mean-squared error. We consider the case of independent...

In this work, we introduce the s,k-extremal coefficients for studying the tail dependence between the s-th lower and k-th upper order statistics of a normalized random vector. If its margins have tail dependence then so do their order statistics, with the strength of bivariate tail dependence...