Explicit covariance matrix for particle measurement precision

Explicit Covariance Matrix for Particle Measurement Precision

We derive explicit and precise formulae for 3 by 3 error matrix of particle transverse momentum, direction and impact parameter. The error matrix elements are expressed as functions of up to fourth order statistical moments of the measured coordinates. The formulae are valid for any curvature and track length in case of negligible multiple scattering. The calculation is compared with formulae d...

More on explicit estimators for a banded covariance matrix

The problem of estimating mean and covariances of a multivariate normally distributed random vector has been studied in many forms. This paper focuses on the estimators proposed by Ohlson et al. (2011) for a banded covariance structure with m-dependence. We rewrite the estimator when m = 1, which makes it easier to analyze. This leads to an adjustment, and an unbiased estimator can be proposed....

Approaches to High-Dimensional Covariance and Precision Matrix Estimation

Nonparametric Eigenvalue-Regularized Precision or Covariance Matrix Estimator

We introduce nonparametric regularization of the eigenvalues of a sample covariance matrix through splitting of the data (NERCOME), and prove that NERCOME enjoys asymptotic optimal nonlinear shrinkage of eigenvalues with respect to the Frobenius norm. One advantage of NERCOME is its computational speed when the dimension is not too large. We prove that NERCOME is positive definite almost surely...

EIGENVECTORS OF COVARIANCE MATRIX FOR OPTIMAL DESIGN OF STEEL FRAMES

In this paper, the discrete method of eigenvectors of covariance matrix has been used to weight minimization of steel frame structures. Eigenvectors of Covariance Matrix (ECM) algorithm is a robust and iterative method for solving optimization problems and is inspired by the CMA-ES method. Both of these methods use covariance matrix in the optimization process, but the covariance matrix calcula...