Related papers: Differentiability of M-functionals of location and…
This paper deals with the asymptotic statistical properties of a class of redescending M-estimators in linear models with increasing dimension. This class is wide enough to include popular high breakdown point estimators such as…
This paper addresses maximum likelihood (ML) estimation based model fitting in the context of extrasolar planet detection. This problem is featured by the following properties: 1) the candidate models under consideration are highly…
Consider a medium characterized by N points whose coordinates are randomly generated by a uniform distribution along the edges of a unitary d-dimensional hypercube. A walker leaves from each point of this disordered medium and moves…
Since its introduction, the skew-$t$ distribution has received much attention in the literature both for the study of theoretical properties and as a model for data fitting in empirical work. A major motivation for this interest is the high…
We consider the Grenander estimator that is the maximum likelihood estimator for non-increasing densities. We prove uniform central limit theorems for certain subclasses of bounded variation functions and for H\"older balls of smoothness…
We propose a new estimation procedure of the conditional density for independent and identically distributed data. Our procedure aims at using the data to select a function among arbitrary (at most countable) collections of candidates. By…
Position probability distribution of a set of massive mutually exclusive particles in one dimension has been defined. Examples with a given two mutually exclusive particles system are considered. It is emphasized that quantum particles at…
Consider a population of $N$ individuals, each having $d\geq 1$ different traits, and an additive measure, called dispersion, which rewards large pairwise separations between traits. The goal is to select $M\leq N$ individuals such that…
We study a random Schroedinger operator, the Laplacian with random Dirac delta potentials on a torus T^d_L = R^d/LZ^d, in the thermodynamic limit L\to\infty, for dimension d=2. The potentials are located on a randomly distorted lattice…
We propose and study properties of maximum likelihood estimators in the class of conditional transformation models. Based on a suitable explicit parameterisation of the unconditional or conditional transformation function, we establish a…
We deal with the equivariant estimation of scatter and location for p-dimensional data, giving emphasis to scatter. It it important that the estimators possess both a high efficiency for normal data and a high resistance to outliers, that…
We state some inequalities for m-divisible and infinite divisible characteristic functions. Basing on them we propose a statistical test for a distribution to be infinitely divisible. Keywords: infinite divisible distributions; statistical…
An inequality of Brascamp-Lieb-Luttinger and of Rogers states that among subsets of Euclidean space $\mathbb{R}^d$ of specified Lebesgue measures, balls centered at the origin are maximizers of certain functionals defined by…
Despite many applications, dimensionality reduction in the $\ell_1$-norm is much less understood than in the Euclidean norm. We give two new oblivious dimensionality reduction techniques for the $\ell_1$-norm which improve exponentially…
Many high-dimensional hypothesis tests aim to globally examine marginal or low-dimensional features of a high-dimensional joint distribution, such as testing of mean vectors, covariance matrices and regression coefficients. This paper…
A pair of probability distributions over $\{0,1\}^n$ is said to be $(k,\delta)$-wise indistinguishable if all of the size $k$ marginals are within statistical distance at most $\delta$. Previous works introduced this concept and study when…
A large dimensional characterization of robust M-estimators of covariance (or scatter) is provided under the assumption that the dataset comprises independent (essentially Gaussian) legitimate samples as well as arbitrary deterministic…
Asymptotic properties of scatter estimators for elliptical graphical models are studied. Such models impose a given pattern of zeros on the inverse of the shape matrix of an elliptically distributed random vector. In particular, we…
M-estimation, aka empirical risk minimization, is at the heart of statistics and machine learning: Classification, regression, location estimation, etc. Asymptotic theory is well understood when the loss satisfies some smoothness…
We completely characterize $\Delta$- and local subexponentialities of positive-half compound Poisson distributions and extend the characterization on two-sided distributions. Moreover, $\Delta$-subexponentiality of infinitely divisible…