Unfortunately, this test shares the poor resistance to nonnormality of its univariate counterpart, and is invalid even under elliptical densities with ﬁnite fourth-order moments: see [12, 38] or .
Optimal rank-based tests for homogeneity of scatter
The effects of nonnormality on asymptotic distributions of some likelihood ratio criteria for testing covariance structures under normal assumption. J.
Optimal rank-based tests for homogeneity of scatter
For the BRCA data of Figure 4, direct inspection of the 3226 by 15 matrix “X ” of expression values reveals markedly nonnormal components, skewed to the right (even after the columns of X have been standardized to mean 0 and standard deviation 1, as in all my examples here).
Microarrays, Empirical Bayes and the Two-Groups Model
This modest contribution also solves the problem of ﬁnding a robust (to nonnormality) alternative to the chi-square variance test for large samples.
asympTest: an R package for performing parametric statistical tests and confidence intervals based on the central limit theorem
However, as shown in Fig. 1, both results become untrue (even approximately) under nonnormality assumption.
asympTest: an R package for performing parametric statistical tests and confidence intervals based on the central limit theorem
The asymptotic distribution of the nonstandardized statistic is nonnormal as expected (see upper panel).
Testing for jumps in a discretely observed process
The case (a) here corresponds to a nonnormal limit with variance 1, and for this limit we cannot evaluate exactly the quantiles and we rely upon the Chebyshev inequality; this is why we only get a bound on the level but not the exact value.
Testing for jumps in a discretely observed process
Here, the function exp(σz 2 ) in the integrand of Eq. (2.15) is sharply peaked at the poles (see Fig. 4), so it can be approximated as a sum of two (nonnormalized) delta functions centered around z = ±1.
On the Statics and Dynamics of Magneto-Anisotropic Nanoparticles
This is due to the fact that the bias and variance are known exactly and not asymptotically; the nonnormality of the statistics for small data sets seems to have lesser effects than approximating the variance.
Testing randomness of spatial point patterns with the Ripley statistic
Its ﬁnite sample unbiasedness is not guaranteed under a nonnormal underlying distribution.
Nonparametric multivariate rank tests and their unbiasedness
Asymptotic distributions in canonical correlation analysis and other multivariate procedures for nonnormal populations.
Efficient ANOVA for directional data
The last two combinations were designed to assess the performance under nonnormality.
Two sample tests for high-dimensional covariance matrices
The simulation results for the proposed test with dimensions much larger than the sample sizes and for nonnormally distributed data are reported in Tables 2–4.
Two sample tests for high-dimensional covariance matrices
We ﬁnd that uncertainties estimated in this direct manner are larger than those estimated from the ∆χ2 contours, possibly due to nonnormal characteristics of the uncertainties in this particular problem (Press et al. 1989).
A Coronal Hole's Effects on CME Shock Morphology in the Inner Heliosphere
Asymptotic theory for principal component analysis: The nonnormal case.
Optimal rank-based testing for principal components
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