78 research outputs found
Likelihood test in permutations with bias. Premier League and La Liga: surprises during the last 25 seasons
In this paper, we introduce the models of permutations with bias, which are
random permutations of a set, biased by some preference values. We present a
new parametric test, together with an efficient way to calculate its p-value.
The final tables of the English and Spanish major soccer leagues are tested
according to this new procedure, to discover whether these results were aligned
with expectations.Comment: Bibliography updated. Thanks to Prof Karlsson to have suggested the
paper [8] H. Stern. Models for distributions on permutations. JASA (1990
A canonical form for Gaussian periodic processes
This article provides a representation theorem for a set of Gaussian
processes; this theorem allows to build Gaussian processes with arbitrary
regularity and to write them as limit of random trigonometric series. We show
via Karhunen-Love theorem that this set is isometrically equivalent to l2. We
then prove that regularity of trajectory path of anyone of such processes can
be detected just by looking at decrease rate of l2 sequence associated to him
via isometry.Comment: 11 pages, 1 figur
A clustering algorithm for multivariate data streams with correlated components
Common clustering algorithms require multiple scans of all the data to
achieve convergence, and this is prohibitive when large databases, with data
arriving in streams, must be processed. Some algorithms to extend the popular
K-means method to the analysis of streaming data are present in literature
since 1998 (Bradley et al. in Scaling clustering algorithms to large databases.
In: KDD. p. 9-15, 1998; O'Callaghan et al. in Streaming-data algorithms for
high-quality clustering. In: Proceedings of IEEE international conference on
data engineering. p. 685, 2001), based on the memorization and recursive update
of a small number of summary statistics, but they either don't take into
account the specific variability of the clusters, or assume that the random
vectors which are processed and grouped have uncorrelated components.
Unfortunately this is not the case in many practical situations. We here
propose a new algorithm to process data streams, with data having correlated
components and coming from clusters with different covariance matrices. Such
covariance matrices are estimated via an optimal double shrinkage method, which
provides positive definite estimates even in presence of a few data points, or
of data having components with small variance. This is needed to invert the
matrices and compute the Mahalanobis distances that we use for the data
assignment to the clusters. We also estimate the total number of clusters from
the data.Comment: title changed, rewritte
A decomposition theorem for fuzzy set-valued random variables and a characterization of fuzzy random translation
Let be a fuzzy set--valued random variable (\frv{}), and \huku{X} the
family of all fuzzy sets for which the Hukuhara difference X\HukuDiff B
exists --almost surely. In this paper, we prove that can be
decomposed as X(\omega)=C\Mink Y(\omega) for --almost every
, is the unique deterministic fuzzy set that minimizes
as is varying in \huku{X}, and is a centered
\frv{} (i.e. its generalized Steiner point is the origin). This decomposition
allows us to characterize all \frv{} translation (i.e. X(\omega) = M \Mink
\indicator{\xi(\omega)} for some deterministic fuzzy convex set and some
random element in \Banach). In particular, is an \frv{} translation if
and only if the Aumann expectation is equal to up to a
translation.
Examples, such as the Gaussian case, are provided.Comment: 12 pages, 1 figure. v2: minor revision. v3: minor revision;
references, affiliation and acknowledgments added. Submitted versio
A new nonlocal nonlinear diffusion equation for image denoising and data analysis
In this paper we introduce and study a new feature-preserving nonlinear
anisotropic diffusion for denoising signals. The proposed partial differential
equation is based on a novel diffusivity coefficient that uses a nonlocal
automatically detected parameter related to the local bounded variation and the
local oscillating pattern of the noisy input signal. We provide a mathematical
analysis of the existence of the solution of our nonlinear and nonlocal
diffusion equation in the two dimensional case (images processing). Finally, we
propose a numerical scheme with some numerical experiments which demonstrate
the effectiveness of the new method
Fractional Poisson Fields and Martingales
We present new properties for the Fractional Poisson process and the
Fractional Poisson field on the plane. A martingale characterization for
Fractional Poisson processes is given. We extend this result to Fractional
Poisson fields, obtaining some other characterizations. The fractional
differential equations are studied. We consider a more general Mixed-Fractional
Poisson process and show that this process is the stochastic solution of a
system of fractional differential-difference equations. Finally, we give some
simulations of the Fractional Poisson field on the plane
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