TY - JOUR

T1 - Likelihood Ratio Tests for Elaborate Covariance Structures and for MANOVA Models with Elaborate Covariance Structures

T2 - A Review

AU - Coelho, Carlos A.

N1 - Funding Information:
info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F00297%2F2020/PT#
Publisher Copyright:
© 2022, Indian Institute of Science.

PY - 2022/4/17

Y1 - 2022/4/17

N2 - In this paper a review is made from the primordia of the history of likelihood ratio tests for covariance structures and equality of mean vectors through the development of likelihood ratio tests that refer to elaborate covariance structures. Relations are established among several covariance structures, taking more elaborate ones as umbrella structures and examining then their particular cases of interest. References are made to bibliography where the corresponding likelihood ratio tests are developed and the distributions of the corresponding statistics addressed. Most of the likelihood ratio test statistics for one-way manova models where the covariance matrices have elaborate structures were developed quite recently. Also for these likelihood ratio tests a similar approach is taken. Although we start with the common test that uses unstructured covariance matrices, then we go on to consider tests with more elaborate covariance structures, and subsequently we specify them to their particular cases of interest. Some special attention is also given to the so-called Wilks Λ statistics.

AB - In this paper a review is made from the primordia of the history of likelihood ratio tests for covariance structures and equality of mean vectors through the development of likelihood ratio tests that refer to elaborate covariance structures. Relations are established among several covariance structures, taking more elaborate ones as umbrella structures and examining then their particular cases of interest. References are made to bibliography where the corresponding likelihood ratio tests are developed and the distributions of the corresponding statistics addressed. Most of the likelihood ratio test statistics for one-way manova models where the covariance matrices have elaborate structures were developed quite recently. Also for these likelihood ratio tests a similar approach is taken. Although we start with the common test that uses unstructured covariance matrices, then we go on to consider tests with more elaborate covariance structures, and subsequently we specify them to their particular cases of interest. Some special attention is also given to the so-called Wilks Λ statistics.

KW - Block compound-symmetry

KW - Block-circularity

KW - Block-diagonal structure

KW - Block-matrix sphericity

KW - Block-scalar sphericity

KW - Double exchangeable structure

KW - Equality mean vectors

KW - Exact distribution

KW - Hyper-block matrix sphericity

KW - Inversion methods

KW - Near-exact distributions

UR - http://www.scopus.com/inward/record.url?scp=85128384428&partnerID=8YFLogxK

UR - https://rdcu.be/cLHwg

U2 - 10.1007/s41745-022-00300-5

DO - 10.1007/s41745-022-00300-5

M3 - Review article

AN - SCOPUS:85128384428

SN - 0970-4140

SP - 1

EP - 39

JO - Journal of the Indian Institute of Science

JF - Journal of the Indian Institute of Science

ER -