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

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

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 comp...

Full description

Saved in:
Bibliographic Details
Published in:Annals of the Institute of Statistical Mathematics Vol. 68; no. 1; pp. 77 - 104
Main Authors: Ducharme, Gilles R., Lafaye de Micheaux, Pierre, Marchina, Bastien
Format: Journal Article
Language:English
Published: Tokyo Springer Japan 01-02-2016
Springer Nature B.V
Springer Verlag
Subjects:
Asymptotic properties
Computer simulation
Economics
Finance
Functions (mathematics)
Insurance
Management
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Monte Carlo simulation
Normal distribution
Packages
Quadratic forms
Random variables
Statistical methods
Statistics
Statistics for Business
Studies
Vectors (mathematics)
Characteristic function
fMRI
Complex multinormal distribution
Complex normality test
Goodness-of-fit test
Quadratic forms
Independence
Complex random vectors
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:0020-3157
1572-9052
DOI:10.1007/s10463-014-0486-5