Related papers: Asymptotic comparison of negative multinomial and …
Exact formulas are derived for the probability density functions of the sum and difference of two independent non-central gamma distributed random variables, with both series and integral representations of the density presented. These…
We study a novel class of affine invariant and consistent tests for normality in any dimension. The tests are based on a characterization of the standard $d$-variate normal distribution as the unique solution of an initial value problem of…
In this paper, we proposed a multivariate normality test based on copula entropy. The test statistic is defined as the difference between the copula entropies of unknown distribution and the Gaussian distribution with same covariances. The…
We study the behavior of the empirical distribution function of iterates of intermittent maps in the Hilbert space of square inegrable functions with respect to Lebesgue measure. In the long-range dependent case, we prove that the empirical…
While the asymptotic normality of the maximum likelihood estimator under regularity conditions is long established, this paper derives explicit bounds for the bounded Wasserstein distance between the distribution of the maximum likelihood…
Dissipation and fluctuations of one-body observables in heavy-ion reactions around the Coulomb barrier are investigated with a microscopic stochastic mean-field approach. By projecting the stochastic mean-field dynamics on a suitable…
Bell's theorem shows that no hidden-variable model can explain the measurement statistics of a quantum system shared between two parties, thus ruling out a classical (local) understanding of nature. In this work we demonstrate that by…
We consider a class of hypothesis testing problems where the null hypothesis postulates $M$ distributions for the observed data, and there is only one possible distribution under the alternative. We show that one can use a stochastic mirror…
Nested sampling is a simulation method for approximating marginal likelihoods proposed by Skilling (2006). We establish that nested sampling has an approximation error that vanishes at the standard Monte Carlo rate and that this error is…
We consider the problem of drawing samples from posterior distributions formed under a Dirichlet prior and a truncated multinomial likelihood, by which we mean a Multinomial likelihood function where we condition on one or more counts being…
The regular variation model for multivariate extremes decomposes the joint distribution of the extremes in polar coordinates in terms of the angles and the norm of the random vector as the product of two independent densities: the angular…
We consider the optimal transport problem between multivariate Gaussian stationary stochastic processes. The transportation effort is the variance of the filtered discrepancy process. The main contribution of this technical note is to show…
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…
The study of sums of possibly associated Bernoulli random variables has been hampered by an asymmetry between positive correlation and negative correlation. The Conway-Maxwell Binomial (COMB) distribution and its multivariate extension, the…
The central limit theorem ensures that a sum of random variables tends to a Gaussian distribution as their total number tends to infinity. However, for a class of positive random variables, we find that the sum tends faster to a log-normal…
Given $n$ independent and identically distributed observations and measuring the value of obtaining an additional observation in terms of Le Cam's notion of deficiency between experiments, we show for certain types of non-parametric…
Gorman and Bedrick (2019) argued for using random splits rather than standard splits in NLP experiments. We argue that random splits, like standard splits, lead to overly optimistic performance estimates. We can also split data in biased or…
This work sheds some light on the relationship between a distribution's standard deviation and its range, a topic that has been discussed extensively in the literature. While many previous studies have proposed inequalities or relationships…
We consider estimation of the covariance matrix of a multivariate random vector under the constraint that certain covariances are zero. We first present an algorithm, which we call Iterative Conditional Fitting, for computing the maximum…
Testing for normality is a widely used procedure in statistics and data analysis, often applied prior to employing methods that rely on the assumption of normally distributed data. While several existing tests target distributional…