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Can Recent Innovations in Harmonic Analysis ‘Explain’ Key Findings in Natural Image Statistics?
Recent Innovations Natural Image Statistics
2015/8/21
Recently, applied mathematicians have been pursuing the goal of sparse coding of
certain mathematical models of images with edges. They have found by mathematical
analysis that, instead of wavelets ...
CENTRAL LIMIT THEOREMS FOR SOME SET PARTITION STATISTICS
Parameters random limit theorem dimension index level
2015/7/7
We prove the conjectured limiting normality for the number of crossings of a uniformly chosen set partition of [n] = f1;2; : : : ; ng. The arguments use a novel stochastic representation and are also ...
A simple variance inequality for U-statistics of a Markov chain with applications
U-statistics Markov chains Inequalities Limit theorems Law of large numbers
2011/9/5
Abstract: We establish a simple variance inequality for U-statistics whose underlying sequence of random variables is an ergodic Markov Chain. The constants in this inequality are explicit and depend ...
Riemannian statistics geometry: A counterpart approach of inference geometry
Geometrical Methods in Statistics Riemannian statistics geometry Statistics Theory
2011/9/5
Abstract: Riemannian statistics geometry is proposed in this work as a counterpart approach of inference geometry. This geometry framework is inspired on the existence of a notable analogy between the...
A procedure for the change point problem in parametric models based on phi-divergence test-statistics
Change point Information criterion Divergence Wald test-statistic General distributions
2011/8/25
Abstract: This paper studies the change point problem for a general parametric, univariate or multivariate family of distributions. An information theoretic procedure is developed which is based on ge...
Time--Evolving Statistics of Chaotic Orbits of Conservative Maps in the Context of the Central Limit Theorem
time Chaotic Orbits Conservative Maps Central Limit Theorem Statistics
2011/7/6
We study chaotic orbits of conservative low--dimensional maps and present numerical results showing that the probability density functions (pdfs) of the sum of $N$ iterates in the large $N$ limit exhi...
Non-Gaussian gravitational clustering field statistics
large-scale structure of Universe – galaxies clusters
2011/3/2
In this work we investigate the multivariate statistical description of the matter distribution
in the nonlinear regime.
Connectivity statistics of store-and-forward inter-vehicle communication
Connectivity statistics store-and-forward inter-vehicle communication
2010/12/28
Inter-vehicle communication (IVC) enables vehicles to exchange messages within a limited broadcast range and thus self-organize into dynamical vehicular ad hoc networks. For
the foreseeable future, h...
Non-Gaussian gravitational clustering field statistics
Non-Gaussian gravitational clustering field statistics
2011/1/4
In this work we investigate the multivariate statistical description of the matter distribution in the nonlinear regime. We introduce the multivariate Edgeworth expansion of the lognormal distribution...
Two-Point Vorticity Statistics in the Inverse Turbulent Cascade
Two-Point Vorticity Statistics Inverse Turbulent Cascade
2010/12/28
We present a statistical analysis of the two-point vorticity probability density of the vorticity eld generated in the inverse cascade of stationary two-dimensional turbulence.
Spectral Statistics of "Cellular" Billiards
Chaotic Dynamics(nlin.CD) Mathematical Physics(math-ph) Spectral Theory(math.SP)
2010/11/10
For a bounded planar domain $\Omega^0$ whose boundary contains a number of flat pieces $\Gamma_i$ we consider a family of non-symmetric billiards $\Omega$ constructed by patching several copies of $\O...
Higher order statistics in the annulus square billiard: transport and polyspectra
Higher order statistics annulus square billiard: transport polyspectra
2010/12/15
Classical transport in a doubly connected polygonal billiard, i.e. the annulus square billiard, is considered. Dynamical properties of the billiard flow with a fixed initial direction are analyzed by ...
U-Quantile Processes and Generalized Linear Statistics of Dependent Data
L-Statistic U-statistics U-quantiles Bahadur representation mixing near epoch dependence
2010/12/14
Generalized linear statistics are a unifying class that contains U-statistics,U-quantiles, L-statistics as well as trimmed and winsorized U-statistics. For example, many commonly used estimators of sc...
In the conviction of Lucia de Berk an important role was played by a simple hypergeometric model, used by the expert consulted by the court, which produced very small probabilities of occurrences of c...
ASYMPTOTIC EFFICIENCY AND LOCAL OPTIMALITY OF DISTRIBUTION { FREE TESTS BASED ON U- AND V-STATISTICS
U-statistics large deviations Bahadur eÆ ciency local optimality.
2014/6/27
Many well-known goodness-of- t and symmetry tests are based on U- et V-statistics. Recent progress in the analysis of their large deviations enables to nd new expressions for their local Bahadur e...