4,608 research outputs found
Weak convergence of the weighted empirical beta copula process
The empirical copula has proved to be useful in the construction and
understanding of many statistical procedures related to dependence within
random vectors. The empirical beta copula is a smoothed version of the
empirical copula that enjoys better finite-sample properties. At the core lie
fundamental results on the weak convergence of the empirical copula and
empirical beta copula processes. Their scope of application can be increased by
considering weighted versions of these processes. In this paper we show weak
convergence for the weighted empirical beta copula process. The weak
convergence result for the weighted empirical beta copula process is stronger
than the one for the empirical copula and its use is more straightforward. The
simplicity of its application is illustrated for weighted Cram\'er--von Mises
tests for independence and for the estimation of the Pickands dependence
function of an extreme-value copula.Comment: 19 pages, 2 figure
Measuring and testing dependence by correlation of distances
Distance correlation is a new measure of dependence between random vectors.
Distance covariance and distance correlation are analogous to product-moment
covariance and correlation, but unlike the classical definition of correlation,
distance correlation is zero only if the random vectors are independent. The
empirical distance dependence measures are based on certain Euclidean distances
between sample elements rather than sample moments, yet have a compact
representation analogous to the classical covariance and correlation.
Asymptotic properties and applications in testing independence are discussed.
Implementation of the test and Monte Carlo results are also presented.Comment: Published in at http://dx.doi.org/10.1214/009053607000000505 the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
A randomness test for functional panels
Functional panels are collections of functional time series, and arise often
in the study of high frequency multivariate data. We develop a portmanteau
style test to determine if the cross-sections of such a panel are independent
and identically distributed. Our framework allows the number of functional
projections and/or the number of time series to grow with the sample size. A
large sample justification is based on a new central limit theorem for random
vectors of increasing dimension. With a proper normalization, the limit is
standard normal, potentially making this result easily applicable in other FDA
context in which projections on a subspace of increasing dimension are used.
The test is shown to have correct size and excellent power using simulated
panels whose random structure mimics the realistic dependence encountered in
real panel data. It is expected to find application in climatology, finance,
ecology, economics, and geophysics. We apply it to Southern Pacific sea surface
temperature data, precipitation patterns in the South-West United States, and
temperature curves in Germany.Comment: Supplemental material from the authors' homepage or upon reques
Measures of Variability for Bayesian Network Graphical Structures
The structure of a Bayesian network includes a great deal of information
about the probability distribution of the data, which is uniquely identified
given some general distributional assumptions. Therefore it's important to
study its variability, which can be used to compare the performance of
different learning algorithms and to measure the strength of any arbitrary
subset of arcs.
In this paper we will introduce some descriptive statistics and the
corresponding parametric and Monte Carlo tests on the undirected graph
underlying the structure of a Bayesian network, modeled as a multivariate
Bernoulli random variable. A simple numeric example and the comparison of the
performance of some structure learning algorithm on small samples will then
illustrate their use.Comment: 19 pages, 4 figures. arXiv admin note: substantial text overlap with
arXiv:0909.168
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