Motivated by problems that arise in computing degrees of belief, we consider the problem of computing asymptotic conditional probabilities for first-order sentences. Given firstorder sentences φ and θ, we consider the structures with domain {1, . . . , N} that satisfy θ, and compute the fraction of them in which φ is true. We then consider what happens to this fraction as N gets large. This ext...

Statistical models for extreme values are generally derived from non-degenerate probabilistic limits that can be used to approximate the distribution of events exceed a selected high threshold. If convergence limit is slow, then approximation may describe observed extremes poorly, and bias only reduced by choosing very threshold at cost unacceptably large variance in any subsequent tail inferen...

The purpose of the paper is to discuss ten things potential users should know about the limits of the Dynamic Conditional Correlation (DCC) representation for estimating and forecasting time-varying conditional correlations. The reasons given for caution about the use of DCC include the following: DCC represents the dynamic conditional covariances of the standardized residuals, and hence does n...

Motivated by problems that arise in computing degrees of belief, we consider the problem of computing asymptotic conditional probabilities for first-order sentences. Given first-order sentences φ and θ, we consider the structures with domain {1, . . . , N} that satisfy θ, and compute the fraction of them in which φ is true. We then consider what happens to this fraction as N gets large. This ex...

0.1 Asymptotic Distribution for Conditional MLE of VARMA Models For a well-defined stationary and invertible VARMA(p, q) model, we assume that the innovations {at} satisfies (a) E(at|Ft−1) = 0, (b) E(atat|Ft−1) = Σ > 0, and (c) at has finite fourth moments, where Ft−1 denotes the σ-field generated by {zt−1, zt−2, · · ·}. It has been proven (Dunsmuir and Hannan, 1976, and Hannan and Deistler, 19...

Tail conditional expectations refer to the expected values of random variables conditioning on some tail events and are closely related to various coherent risk measures. In the univariate case, the tail conditional expectation is asymptotically proportional to the value-at-risk, a popular risk measure. The focus of this paper is on asymptotic relations between the multivariate tail conditional...

A closed subspace V of L 2 := L 2 (IR d) is called PSI (principal shift-invariant) if it is the smallest space that contains all the shifts (i.e., integer translates) of some function 2 L 2. Ideally, each function f in such PSI V can be written uniquely as a convergent series f = X 2ZZ d c()(?) with kck`2 kfk L 2. In this case one says that the shifts of form a Riesz basis or that they are L 2-...

We study stochastic perturbations of ODEs with stable limit cycles — referred to as oscillators and investigate the response asymptotic (in time) frequency oscillations changing noise amplitude. Unlike previous studies, we do not restrict our attention small-noise limit, account for fact that large deviation events may push system out its oscillatory regime. To so, consider conditioned on their...

In a nonparametric setup involving stochastic regressors. regression quantiles relate to the so called conditional quantile functions. Various asymptotic properties of such conditional quantile processes are studied with due emphasis on the underlying design aspects.