107 research outputs found
Testing multivariate uniformity based on random geometric graphs
We present new families of goodness-of-fit tests of uniformity on a
full-dimensional set based on statistics related to edge lengths
of random geometric graphs. Asymptotic normality of these statistics is proven
under the null hypothesis as well as under fixed alternatives. The derived
tests are consistent and their behaviour for some contiguous alternatives can
be controlled. A simulation study suggests that the procedures can compete with
or are better than established goodness-of-fit tests. We show with a real data
example that the new tests can detect non-uniformity of a small sample data
set, where most of the competitors fail.Comment: 36 pages, 2 figure
Tests for multivariate normality -- a critical review with emphasis on weighted -statistics
This article gives a synopsis on new developments in affine invariant tests
for multivariate normality in an i.i.d.-setting, with special emphasis on
asymptotic properties of several classes of weighted -statistics. Since
weighted -statistics typically have limit normal distributions under fixed
alternatives to normality, they open ground for a neighborhood of model
validation for normality. The paper also reviews several other invariant tests
for this problem, notably the energy test, and it presents the results of a
large-scale simulation study. All tests under study are implemented in the
accompanying R-package mnt
Tests for multivariate normality—a critical review with emphasis on weighted -statistics
This article gives a synopsis on new developments in affine invariant tests for multivariate normality in an i.i.d.-setting, with special emphasis on asymptotic properties of several classes of weighted L-statistics. Since weighted L-statistics typically have limit normal distributions under fixed alternatives to normality, they open ground for a neighborhood of model validation for normality. The paper also reviews several other invariant tests for this problem, notably the energy test, and it presents the results of a large-scale simulation study. All tests under study are implemented in the accompanying R-package mnt
Independent additive weighted bias distributions and associated goodness-of-fit tests
We use a Stein identity to define a new class of parametric distributions
which we call ``independent additive weighted bias distributions.'' We
investigate related -type discrepancy measures, empirical versions of
which not only encompass traditional ODE-based procedures but also offer novel
methods for conducting goodness-of-fit tests in composite hypothesis testing
problems. We determine critical values for these new procedures using a
parametric bootstrap approach and evaluate their power through Monte Carlo
simulations. As an illustration, we apply these procedures to examine the
compatibility of two real data sets with a compound Poisson Gamma distribution
On the eigenvalues associated with the limit null distribution of the Epps-Pulley test of normality
The Shapiro–Wilk test (SW) and the Anderson–Darling test (AD) turned out to be strong procedures for testing for normality. They are joined by a class of tests for normality proposed by Epps and Pulley that, in contrast to SW and AD, have been extended by Baringhaus and Henze to yield easy-to-use affine invariant and universally consistent tests for normality in any dimension. The limit null distribution of the Epps–Pulley test involves a sequences of eigenvalues of a certain integral operator induced by the covariance kernel of a Gaussian process. We solve the associated integral equation and present the corresponding eigenvalues
A Monte Carlo study of random surface field effect on layering transitions
The effect of a random surface field, within the bimodal distribution, on the
layering transitions in a spin-1/2 Ising thin film is investigated, using Monte
Carlo simulations. It is found that the layering transitions depend strongly on
the concentration of the disorder of the surface magnetic field, for a
fixed temperature, surface and external magnetic fields. Indeed, the critical
concentration at which the magnetisation of each layer changes the
sign discontinuously, decreases for increasing the applied surface magnetic
field, for fixed values of the temperature and the external magnetic field
. Moreover, the behaviour of the layer magnetisations as well as the
distribution of positive and negative spins in each layer, are also established
for specific values of , , and the temperature . \\Comment: 5 pages latex, 6 figures postscrip
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