Structure identification for a linearly structured covariance matrix

Abstract

Summary Linearly structured covariance matrices are widely used in multivariate analysis. The covariance structure can be chosen from a class of linear structures. Therefore, the optimal structure is identified in terms of minimizing the discrepancy function. In this research, the entropy loss function is used as the discrepancy function. We give a methodology and algorithm for determining the optimal structure from the class of structures under consideration. The accuracy of the proposed method is checked using a simulation study.

Structure identification for a linearly structured covariance matrix: part II

“…We can observe that the T 2 structure is not contained within any other of the structures considered (we know that T 1 ⊂ T 2 and CS ⊂ CS_T 1 ). In the work Mieldzioc (2022) the covariance matrix Σ had the CS_T 1 structure and the results for x close to 0 were very similar to the results for the CS structure.…”

“…In this paper we continue the research from Mieldzioc (2022) about structure identification of a linearly structured covariance matrix under matrix normal distribution. We present new results based on simulation studies, where the covariance matrix Σ has a pentadiagonal banded Toeplitz structure.…”

“…The algorithm for the determination of the minimum entropy loss function of a linear structure B is given in Mieldzioc (2022) and is written as follows Algorithm 1 (Newton's method). For a given starting point α and tolerance ϵ, repeat:…”

Estimation methods for a linearly structured covariance matrix

“…In this paper, we continue the research presented in Mieldzioc (2022) where the linear structure of a covariance matrix was identified. As the next step, when the structure has already been chosen, one may be interested in estimation methods that lead to an estimate having good statistical properties.…”

“…Since this is a continuation of work by Mieldzioc (2022), we will make the same assumptions about the model. Suppose that we observe n independent and identically distributed m-dimensional random vectors X 1 , X 2 , .…”