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 -