Characterizations of joint distributions, copulas, information, dependence and decoupling, with applications to time series

Mathematics – Statistics Theory

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

Published at http://dx.doi.org/10.1214/074921706000000455 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/

Scientific paper

10.1214/074921706000000455

In this paper, we obtain general representations for the joint distributions and copulas of arbitrary dependent random variables absolutely continuous with respect to the product of given one-dimensional marginal distributions. The characterizations obtained in the paper represent joint distributions of dependent random variables and their copulas as sums of $U$-statistics in independent random variables. We show that similar results also hold for expectations of arbitrary statistics in dependent random variables. As a corollary of the results, we obtain new representations for multivariate divergence measures as well as complete characterizations of important classes of dependent random variables that give, in particular, methods for constructing new copulas and modeling different dependence structures. The results obtained in the paper provide a device for reducing the analysis of convergence in distribution of a sum of a double array of dependent random variables to the study of weak convergence for a double array of their independent copies. Weak convergence in the dependent case is implied by similar asymptotic results under independence together with convergence to zero of one of a series of dependence measures including the multivariate extension of Pearson's correlation, the relative entropy or other multivariate divergence measures. A closely related result involves conditions for convergence in distribution of $m$-dimensional statistics $h(X_t,X_{t+1},...,X_{t+m-1})$ of time series $\{X_t\}$ in terms of weak convergence of $h(\xi_t,\xi_{t+1},...,\xi_{t+m-1})$, where $\{\xi_t\}$ is a sequence of independent copies of $X_t'$s, and convergence to zero of measures of intertemporal dependence in $\{X_t\}$. The tools used include new sharp estimates for the distance between the distribution function of an arbitrary statistic in dependent random variables and the distribution function of the statistic in independent copies of the random variables in terms of the measures of dependence of the random variables. Furthermore, we obtain new sharp complete decoupling moment and probability inequalities for dependent random variables in terms of their dependence characteristics.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Characterizations of joint distributions, copulas, information, dependence and decoupling, with applications to time series does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Characterizations of joint distributions, copulas, information, dependence and decoupling, with applications to time series, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Characterizations of joint distributions, copulas, information, dependence and decoupling, with applications to time series will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-617818

All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.