Linear discrimination with equicorrelated training vectors

Abstract

Fisher's linear discrimination rule requires uncorrelated training vectors. In this paper a linear discrimination method is developed to be used when the training vectors are equicorrelated. Also, maximum likelihood ratio tests are proposed to decide whether the training samples are uncorrelated or equicorrelated.

Optimal estimation for doubly multivariate data in blocked compound symmetric covariance structure

“…These authors also discussed the inferential procedures for interclass and intraclass correlations in the multivariate situation for more than one characteristic by proposing some unified estimators and derived the asymptotic distributions of these estimators. Afterwards BCS covariance structure did not attract much attention in the literature for some time until Leiva [15] developed classification rules for doubly multivariate observations and generalized Fisher's linear discrimination method assuming BCS covariance structure, which he named as equicorrelated covariance structure, for the data. Leiva [15] derived maximum likelihood estimates (MLEs) of the BCS covariance structure and developed classification rules using these MLEs.…”

“…Afterwards BCS covariance structure did not attract much attention in the literature for some time until Leiva [15] developed classification rules for doubly multivariate observations and generalized Fisher's linear discrimination method assuming BCS covariance structure, which he named as equicorrelated covariance structure, for the data. Leiva [15] derived maximum likelihood estimates (MLEs) of the BCS covariance structure and developed classification rules using these MLEs. Lately, this covariance structure started gaining a lot of attention in the literature, especially in the area of high-dimensional estimation (see [27]).…”

Testing the equality of mean vectors for paired doubly multivariate observations in blocked compound symmetric covariance matrix setup

“…We also assume that 0 is constant for all sites and 1 is constant for all site pairs. The matrix is also known as equicorrelated partitioned matrix with equicorrelation matrices 0 and 1 [6,18].…”

Discrimination with jointly equicorrelated multi-level multivariate data

“…In this article we develop both linear and quadratic discriminant functions, for multi-level multivariate data, in particular for three-level multivariate data by introducing a parsimonious "jointly equicorrelated covariance" structure (Leiva 2007). Jointly equicorrelated covariance structure (defined in Sect.…”

“…Afterward, Roy (2006) extended the problem of classification of doubly multivariate data to the case of missing data in a mixed model set up. Roy and Leiva (2006) in an unpublished work further extended the problem in the triply multivariate scenario or for three-level multivariate data, by using an "equicorrelated (partitioned) matrix" (Leiva 2007) on the measurement vector over sites, in addition to an AR(1) correlation structure on the repeated measurements over time. In their paper Roy and Leiva…”