A Goodness-of-Fit Test for Elliptical Distributions with Diagnostic Capabilities

This paper develops a smooth test of goodness-of-fit for elliptical distributions. The test is adaptively omnibus, invariant to affine-linear transformations and has a convenient expression that can be broken into components. These components have diagnostic capabilities and can be used to identify specific departures. This helps in correcting the null model when the test rejects. As an example, the results are applied to the multivariate normal distribution for which the R package ECGofTestDx is available. It is shown that the proposed test strategy encompasses and generalizes a number of existing approaches. Some other cases are studied, such as the bivariate Laplace, logistic and Pearson type II distribution. A simulation experiment shows the usefulness of the diagnostic tools

Goodness-of-fit tests of normality for the innovations in ARMA models

International audienc

A Goodness-of-Fit Test for Elliptical Distributions with Diagnostic Capabilities

This paper develops a smooth test of goodness-of-fit for elliptical distributions. The test is adaptively omnibus, invariant to affine-linear transformations and has a convenient expression that can be broken into components. These components have diagnostic capabilities and can be used to identify specific departures. This helps in correcting the null model when the test rejects. As an example, the results are applied to the multivariate normal distribution for which the R package ECGofTestDx is available. It is shown that the proposed test strategy encompasses and generalizes a number of existing approaches. Some other cases are studied, such as the bivariate Laplace, logistic and Pearson type II distribution. A simulation experiment shows the usefulness of the diagnostic tools

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

International audienceThis 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

Nonparametric

tests of independence between random vector