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

Authors:
Filipe J. Marques;Carlos A. Coelho
Affiliations:
Mathematics Department, Faculty of Science and Technology and Centro de Matemática e Aplicações, Nova University of Lisbon, Caparica, Portugal;Mathematics Department, Faculty of Science and Technology and Centro de Matemática e Aplicações, Nova University of Lisbon, Caparica, Portugal
Venue:
Computational Statistics
Year:
2013

Citing 5
Cited 0

The generalized integer Gamma distribution—a basis for distributions in multivariate statistics

Journal of Multivariate Analysis
The generalized near-integer Gamma distribution: a basis for 'near-exact' approximations to the distribution of statistics which are the product of an odd number of independent Beta random variables

Journal of Multivariate Analysis
Toeplitz and circulant matrices: a review

Communications and Information Theory
Near-exact distributions for the independence and sphericity likelihood ratio test statistics

Journal of Multivariate Analysis
The distribution of the product of powers of independent uniform random variables - A simple but useful tool to address and better understand the structure of some distributions

Journal of Multivariate Analysis

Quantified Score

Hi-index	0.00

Visualization

Abstract

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.