Related papers: Are You All Normal? It Depends!
There is a wide availability of methods for testing normality under the assumption of independent and identically distributed data. When data are dependent in space and/or time, however, assessing and testing the marginal behavior is…
We propose a simple multivariate normality test based on Kac-Bernstein's characterization, which can be conducted by utilising existing statistical independence tests for sums and differences of data samples. We also perform its empirical…
Extensive literature exists on how to test for normality, especially for identically and independently distributed (i.i.d) processes. The case of dependent samples has also been addressed, but only for scalar random processes. For this…
Most normality tests in the literature are performed for scalar and independent samples. Thus, they become unreliable when applied to colored processes, hampering their use in realistic scenarios.We focus on Mardia's multivariate kurtosis,…
In this article, we consider the problem of simultaneous testing of hypotheses when the individual test statistics are not necessarily independent. Specifically, we consider the problem of simultaneous testing of point null hypotheses…
We propose new affine invariant tests for multivariate normality, based on independence characterizations of the sample moments of the normal distribution. The test statistics are obtained using canonical correlations between sets of sample…
Testing for dependence has been a well-established component of spatial statistical analyses for decades. In particular, several popular test statistics have desirable properties for testing for the presence of spatial autocorrelation in…
Score-based tests have been used to study parameter heterogeneity across many types of statistical models. This chapter describes a new self-normalization approach for score-based tests of mixed models, which addresses situations where…
We consider the problem of testing multivariate normality when the data consists of a random sample of two-step monotone incomplete observations. We define for such data a generalization of Mardia's statistic for measuring kurtosis, derive…
Performances of the Multivariate Kurtosis are investigated when applied to colored data, with or without Auto-Regressive pre-whitening, and with or without projection onto a lower-dimensional random subspace. Computer experiments…
In this article we prove a generalization of the Ejsmont characterization of the multivariate normal distribution. Based on it, we propose a new test for independence and normality. The test uses an integral of the squared modulus of the…
In public health applications, spatial data collected are often recorded at different spatial scales and over different correlated variables. Spatial change of support is a key inferential problem in these applications and have become…
This study presents a new procedure for necessary tests of multivariate normality based on the uniform distribution on the Stiefel manifold. We demonstrate that the test statistic, which is formed by the product of the scaled residual…
We present new families of goodness-of-fit tests of uniformity on a full-dimensional set $W\subset\R^d$ based on statistics related to edge lengths of random geometric graphs. Asymptotic normality of these statistics is proven under the…
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 $L^2$-statistics. Since weighted…
Spatial association measures for univariate static spatial data are widely used. When the data is in the form of a collection of spatial vectors with the same temporal domain of interest, we construct a measure of similarity between the…
In this paper, our interest is in the problem of simultaneous hypothesis testing when the test statistics corresponding to the individual hypotheses are possibly correlated. Specifically, we consider the case when the test statistics…
Many statistical methodologies for high-dimensional data assume the population is normal. Although a few multivariate normality tests have been proposed, to the best of our knowledge, none of them can properly control the type I error when…
Two-sample tests for multivariate data and especially for non-Euclidean data are not well explored. This paper presents a novel test statistic based on a similarity graph constructed on the pooled observations from the two samples. It can…
We develop a test of normality for spatially indexed functions. The assumption of normality is common in spatial statistics, yet no significance tests, or other means of assessment, have been available for functional data. This paper aims…