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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 ...
OPTIMAL AND FAST DETECTION OF SPATIAL CLUSTERS WITH SCAN STATISTICS
SPATIAL CLUSTERS SCAN STATISTICS
2015/8/20
We consider the detection of multivariate spatial clusters in the Bernoulli
model with N locations, where the design distribution has weakly dependent
marginals. The locations are scanned with a rec...
ON the Statistics of Cision:The Julesz Conjecture.
Theorise of Data Analysis:From Magical Thinking Through Classical Statistics
Establish theory data analysis the classical statistics magical thinking
2015/7/14
Theorise of Data Analysis:From Magical Thinking Through Classical Statistics。
CLOSED EXPRESSIONS FOR AVERAGES OF SET PARTITION STATISTICS
Points theory triangular matrix the mean linear transfer fluid
2015/7/7
In studying the enumerative theory of super characters of the group of upper triangular matrices over a finite field we found that the moments (mean, variance and
higher moments) of novel...
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 ...
Random matrices: Universality of local spectral statistics of non-Hermitian matrices
Random matrices non-Hermitian matrices Probability
2012/6/30
It is a classical result of Ginibre that the normalized bulk $k$-point correlation functions of a complex $n \times n$ gaussian matrix with independent entries of mean zero and unit variance are asymp...
Central limit theorem for partial linear eigenvalue statistics of Wigner matrices
Central limit theorem partial linear eigenvalue statistics Wigner matrices Probability
2012/6/19
In this paper, we study the complex Wigner matrices $M_n=\frac{1}{\sqrt{n}}W_n$ whose eigenvalues are typically in the interval $[-2,2]$. Let $\lambda_1\leq \lambda_2...\leq\lambda_n$ be the ordered e...
Local statistics of lattice points on the sphere
Local statistics lattice points sphere Number Theory
2012/4/17
We study the spatial distribution of the representation of a large integer as a sum of three squares, on the small and critical scale as well as their electrostatic energy. The main results announced ...
Characterizations of distributions via order statistics with random exponential shifts
characterizations order statistics exponential distribution generalized logistic distribution
2011/9/19
Abstract: A class of probability distributions is characterized via equalities in law between two order statistics shifted by independent exponential variables. An explicit formula for the quintile fu...
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...
Change point analysis of an exponential model based on Phi-divergence test-statistics: simulated critical points case
Change point Exponential model Likelihood ratio test Power-divergence test statistic
2011/8/25
Abstract: Recently Batsidis \textit{et al.} (2011) have presented a new procedure based on divergence measures for testing the hypothesis of the existence of a change point in exponential populations....
A CLT for Information-theoretic statistics of Non-centered Gram random matrices
Random Matrix Spectral measure Stieltjes Transform Central Limit Theorem
2011/8/22
Abstract: In this article, we study the fluctuations of the random variable: $$ {\mathcal I}_n(\rho) = \frac 1N \log\det(\Sigma_n \Sigma_n^* + \rho I_N),\quad (\rho>0) $$ where $\Sigma_n= n^{-1/2} D_n...