TY - JOUR

T1 - Obtaining the exact and near-exact distributions of the likelihood ratio statistic to test circular symmetry through the use of characteristic functions

AU - Marques, Filipe José Gonçalves Pereira

AU - Coelho, Carlos Manuel Agra

PY - 2013/1/1

Y1 - 2013/1/1

N2 - In this paper the authors show how through the use of the characteristic function of the negative logarithm of the likelihood ratio test (l.r.t.) statistic to test circular symmetry it is possible to obtain highly manageable expressions for the exact distribution of such statistic, when the number of variables, p, is odd, and highly manageable and accurate approximations for an even p. For the case of an even p, two kinds of near-exact distributions are developed for the l.r.t. statistic which correspond, for the logarithm of the l.r.t. statistic, to a Generalized Near-Integer Gamma distribution or finite mixtures of these distributions. Numerical studies conducted in order to assess the quality of these new approximations show their impressive performance, namely when compared with the only available asymptotic distribution in the literature.

AB - In this paper the authors show how through the use of the characteristic function of the negative logarithm of the likelihood ratio test (l.r.t.) statistic to test circular symmetry it is possible to obtain highly manageable expressions for the exact distribution of such statistic, when the number of variables, p, is odd, and highly manageable and accurate approximations for an even p. For the case of an even p, two kinds of near-exact distributions are developed for the l.r.t. statistic which correspond, for the logarithm of the l.r.t. statistic, to a Generalized Near-Integer Gamma distribution or finite mixtures of these distributions. Numerical studies conducted in order to assess the quality of these new approximations show their impressive performance, namely when compared with the only available asymptotic distribution in the literature.

KW - Mixtures

KW - Near-exact distributions

KW - Generalized Near-Integer Gamma distribution

KW - Asymptotic distributions

KW - Generalized Integer Gamma distribution

KW - Circular symmetry

U2 - 10.1007/s00180-013-0398-5

DO - 10.1007/s00180-013-0398-5

M3 - Article

SN - 0943-4062

VL - 28

SP - 2091

EP - 2115

JO - Computational Statistics

JF - Computational Statistics

IS - 5

ER -