TY - JOUR

T1 - Near-exact distributions for the likelihood ratio test statistic to test equality of several variance-covariance matrices in elliptically contoured distributions

AU - Coelho, Carlos Manuel Agra

AU - Marques, Filipe José Gonçalves Pereira

PY - 2012/1/1

Y1 - 2012/1/1

N2 - The exact distribution of the likelihood ratio test statistic to test the equalityof several variance-covariance matrices has a non-manageable form.On the other hand, the existing asymptotic approximations do not exhibit the necessary precision for many applications. For these reasons, the development of near-exact approximations to the distribution of this statistic, arising from a different method of approximating distributions,emerges as a desirable goal. These distributions, while being manageable are much closer to the exact distribution than the usual asymptotic distributions and opposite to these, are also asymptotic for increasing number of variables and matrices involved. Computational modules to implement the near-exact distributions are made available on a web-site.

AB - The exact distribution of the likelihood ratio test statistic to test the equalityof several variance-covariance matrices has a non-manageable form.On the other hand, the existing asymptotic approximations do not exhibit the necessary precision for many applications. For these reasons, the development of near-exact approximations to the distribution of this statistic, arising from a different method of approximating distributions,emerges as a desirable goal. These distributions, while being manageable are much closer to the exact distribution than the usual asymptotic distributions and opposite to these, are also asymptotic for increasing number of variables and matrices involved. Computational modules to implement the near-exact distributions are made available on a web-site.

KW - Sum of gamma distributions

KW - Mixtures

KW - Asymptotic approximations

KW - Generalized near-integer gamma distribution

KW - Product of beta distributions

U2 - 10.1007/s00180-011-0281-1

DO - 10.1007/s00180-011-0281-1

M3 - Article

VL - 27

SP - 627

EP - 659

JO - Computational Statistics

JF - Computational Statistics

SN - 0943-4062

IS - 4

ER -