TY - CHAP

T1 - The Block-Matrix Sphericity Test: Exact and Near-Exact Distributions for the Test Statistic

AU - Marques, Filipe José Gonçalves Pereira

AU - Coelho, Carlos Manuel Agra

N1 - Springer: "This volume contains a selection of contributions presented at the XVIII Annual Congress of the Portuguese Statistical Society."
Os autores dizem: "Os Capítulos deste livro ainda não estão de facto indexados na ISI-WOS, mas foi-nos assegurado pela Springer que deverão ser indexados em breve."
Não encontrei nenhum dos outros volumes da série indexado na ISI-WoS.

PY - 2013/1/1

Y1 - 2013/1/1

N2 - In this work near-exact distributions for the likelihood ratio test (l.r.t.) statistic to test the one sample block-matrix sphericity hypothesis are developed under the assumption of multivariate normality. Using a decomposition of the null hypothesis in two null hypotheses, one for testing the independence of the k groups of variables and the other one for testing the equality of the k block diagonal matrices of the covariance matrix, we are able to derive the expressions of the l.r.t. statistic, its h-th null moment, and the characteristic function (c.f.) of its negative logarithm. The decomposition of the null hypothesis induces a factorization on the c.f. of the negative logarithm of the l.r.t. statistic that enables us to obtain near-exact distributions for the l.r.t. statistic. Numerical studies using a measure based on the exact and approximating c.f.'s are developed. This measure is an upper bound on the distance between the exact and approximating distribution functions, and it is used to assess the performance of the near-exact distributions and to compare these with the Box type asymptotic approximation developed by Chao and Gupta (Commun. Stat. Theory Methods 20:1957-1969, 1991).

AB - In this work near-exact distributions for the likelihood ratio test (l.r.t.) statistic to test the one sample block-matrix sphericity hypothesis are developed under the assumption of multivariate normality. Using a decomposition of the null hypothesis in two null hypotheses, one for testing the independence of the k groups of variables and the other one for testing the equality of the k block diagonal matrices of the covariance matrix, we are able to derive the expressions of the l.r.t. statistic, its h-th null moment, and the characteristic function (c.f.) of its negative logarithm. The decomposition of the null hypothesis induces a factorization on the c.f. of the negative logarithm of the l.r.t. statistic that enables us to obtain near-exact distributions for the l.r.t. statistic. Numerical studies using a measure based on the exact and approximating c.f.'s are developed. This measure is an upper bound on the distance between the exact and approximating distribution functions, and it is used to assess the performance of the near-exact distributions and to compare these with the Box type asymptotic approximation developed by Chao and Gupta (Commun. Stat. Theory Methods 20:1957-1969, 1991).

M3 - Chapter

SN - 978-3-642-32418-5 / 978-3-642-32419-2

T3 - Studies in Theoretical and Applied Statistics

SP - 169

EP - 177

BT - Recent Developments in Modeling and Applications in Statistics

A2 - Oliveira, Paulo Eduardo

A2 - Temido, Maria da Graça

A2 - Henriques, Carla

A2 - Vichi, Maurizio

PB - Springer

CY - Heidelberg

ER -