Related papers: Semicircle Law for Tyler's M-Estimator of Scatter
We propose estimating the scale parameter (mean of the eigenvalues) of the scatter matrix of an unspecified elliptically symmetric distribution using weights obtained by solving Tyler's M-estimator of the scatter matrix. The proposed…
A part of Moliere's multiple scattering theory concerning the determination of the screening angular parameter is revised. An universal form of the Coulomb corrections to the screening angle, the exponential part of the distribution…
Tyler's and Maronna's M-estimators, as well as their regularized variants, are popular robust methods to estimate the scatter or covariance matrix of a multivariate distribution. In this work, we study the non-asymptotic behavior of these…
This is the first of two subsequent publications where the probability distribution of delay-times in scattering of wave packets is discussed. The probability distribution is expressed in terms of the on-shell scattering matrix, the…
Elliptically symmetric distributions are widely used in portfolio modeling, as well as in signal processing applications for modeling impulsive background noises. Of particular interest are algorithms for covariance estimation and subspace…
We show that the probability distribution corresponding to a fully random tracial state of a system of spin-S particles satisfies a diffusion-like equation. The diffusion coefficient turns out to be equal to $S(S+1)/6$, where $S$ is the…
We present a general algorithm to show that a scattering operator associated to a semilinear dispersive equation is real analytic, and to compute the coefficients of its Taylor series at any point. We illustrate this method in the case of…
In this paper in a framework of classical electrodynamics, we re-derived in a simple way the formula for the light scattering by moving particle with arbitrary angle of collision.
We establish a link between the phenomenon of Taylor dispersion and the theory of empirical distributions. Using this connection, we derive, upon applying the theory of large deviations, an alternative and much more precise description of…
The joint estimation of means and scatter matrices is often a core problem in multivariate analysis. In order to overcome robustness issues, such as outliers from Gaussian assumption, M-estimators are now preferred to the traditional sample…
For a class of random matrix ensembles with correlated matrix elements, it is shown that the density of states is given by the Wigner semi-circle law. This is applied to effective Hamiltonians related to the Anderson model in dimensions…
In this paper, a general class of regularized $M$-estimators of scatter matrix are proposed which are suitable also for low or insufficient sample support (small $n$ and large $p$) problems. The considered class constitutes a natural…
A fundamental problem in statistics is estimating the shape matrix of an Elliptical distribution. This generalizes the familiar problem of Gaussian covariance estimation, for which the sample covariance achieves optimal estimation error.…
We developed a Monte Carlo simulation method to calculate incoherent Thomson scattering spectra in high temperature plasmas. The basic idea is to treat the entire scattering process as the superposition of individual photon-electron…
In this paper we consider a new normalization of matrices obtained by choosing distinct codewords at random from linear codes over finite fields and find that under some natural algebraic conditions of the codes their empirical spectral…
In this paper, convergence rates of the spectral distributions of quaternion self-dual Hermitian matrices are investigated. We show that under conditions of finite 6th moments, the expected spectral distribution of a large quaternion…
We prove that solutions to the quintic semilinear wave equation with variable coefficients in $\mathbb R^{1+3}$ scatter to a solution to the corresponding linear wave equation. The coefficients are small and decay as $|x|\to\infty$, but are…
We prove Strichartz estimates (both regular and reversed) for a scattering state to the wave equation with a charge transfer Hamiltonian in $\mathbb{R}^{3}$: \[ \partial_{tt}u-\Delta u+\sum_{j=1}^{m}V_{j}\left(x-\vec{v}_{j}t\right)u=0. \]…
We derive the off-shell scattering matrix for a spherical scatterer. The result obtained generalizes the off-on-shell matrix commonly used in the theory of scalar waves propagation in random media.
We give a probabilistic numerical method for solving a partial differential equation with fractional diffusion and nonlinear drift. The probabilistic interpretation of this equation uses a system of particles driven by L\'evy alpha-stable…