The covariance matrix of a pattern is composed by its second order central moments. For a rotationally symmetric shape, its covariance matrix is a scalar identity matrix. In this work, we apply this property to restore the skewed shape of rotational symmetry. The relations between the skew transformation matrix and the covariance matrices of original and skewed shapes are derived. By computing ...

This article analyzes whether the existing tests for the p× p covariance matrix Σ of the N independent identically distributed observation vectors with N ≤ p work under non-normality. We focus on three hypotheses testing problems: (1) testing for sphericity, that is, the covariance matrix Σ is proportional to an identity matrix Ip; (2) the covariance matrix Σ is an identity matrix Ip; and (3) t...

Estimating a covariance matrix efficiently and discovering its structure are important statistical problems with applications in many fields. This article takes a Bayesian approach to estimate the covariance matrix of Gaussian data. We use ideas from Gaussian graphical models and model selection to construct a prior for the covariance matrix that is a mixture over all decomposable graphs, where...

A covariance matrix is a tool that expresses the odometry uncertainty of mobile robots. The covariance matrix is a key factor in various localization algorithms such as the Kalman filter or topological matching. However, it is not easy to acquire an accurate covariance matrix because the real states of robots are not known. Till now, few results on estimating the covariance matrix have been rep...

Diiculties in computing the posterior distribution of a covariance matrix when using nonconjugate priors has been discussed by several authors. Typically, the posterior distribution for the covariance matrix is computed via the Gibbs sampler and when using a Wishart prior for the inverse of the covariance matrix, one obtains conditional conjugacy (the full conditional distribution of the invers...

Estimating a covariance matrix is an important task in applications where the number of variables is larger than the number of observations. In the literature, shrinkage approaches for estimating a high-dimensional covariance matrix are employed to circumvent the limitations of the sample covariance matrix. A new family of nonparametric Stein-type shrinkage covariance estimators is proposed who...