The complex multinormal distribution, quadratic forms in complex random vectors and an omnibus goodness-of-fit test for the complex normal distribution

Autor: Pierre Lafaye de Micheaux, Bastien Marchina, Gilles R. Ducharme
Přispěvatelé: Institut Montpelliérain Alexander Grothendieck (IMAG), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), Département de Mathématiques et de Statistiques [UdeM- Montréal], Université de Montréal (UdeM), Méthodologie Statistique et Sciences Sociales (MS3), Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])
Rok vydání: 2014
Předmět:
Zdroj: Annals of the Institute of Statistical Mathematics
Annals of the Institute of Statistical Mathematics, Springer Verlag, 2016, 68 (1), pp.77-104. ⟨10.1007/s10463-014-0486-5⟩
Annals of the Institute of Statistical Mathematics, 2016, 68 (1), pp.77-104. ⟨10.1007/s10463-014-0486-5⟩
ISSN: 1572-9052
0020-3157
DOI: 10.1007/s10463-014-0486-5
Popis: International audience; This paper first reviews some basic properties of the (noncircular) complex multinormal distribution and presents a few characterizations of it. The distribution of linear combinations of complex normally distributed random vectors is then obtained, as well as the behavior of quadratic forms in complex multinormal random vectors. We look into the problem of estimating the complex parameters of the complex normal distribution and give their asymptotic distribution. We then propose a virtually omnibus goodness-of-fit test for the complex normal distribution with unknown parameters, based on the empirical characteristic function. Monte Carlo simulation results show that our test behaves well against various alternative distributions. The test is then applied to an fMRI data set and we show how it can be used to “validate” the usual hypothesis of normality of the outside-brain signal. An R package that contains the functions to perform the test is available from the authors.
Databáze: OpenAIRE
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