The theory of local asymptotic normality for quantum statistical experiments is developed in the spirit of the classical result from mathematical statistics due to Le Cam. Roughly speaking, local asymptotic normality means that the family φ θ0+u/ √ n consisting of joint states of n identically prepared quantum systems approaches in a statistical sense a family of Gaussian state φu of an algebra...

The theory of local asymptotic normality for quantum statistical experiments is developed in the spirit of the classical result from mathematical statistics due to Le Cam. Roughly speaking, local asymptotic normality means that the family φnθ0+u/ √ n consisting of joint states of n identically prepared quantum systems approaches in a statistical sense a family of Gaussian state φu of an algebra...

We propose U -statistics-based tests for null variance components in linear mixed models. We obtain their asymptotic distribution (for increasing number of units) under mild regularity conditions that include only the existence of the second moment for the distribution of the random effects and of the fourth moment for the distribution of the conditional errors. We also derive their nonnull dis...

Assessing the assumption of multivariate normality is required by many parametric multivariate statistical methods, such as discriminant analysis, principal component analysis, MANOVA, etc. Here, we present an R package to asses multivariate normality. The MVN package contains three most widely used multivariate normality tests, including Mardia’s, Henze-Zirkler’s and Royston’s multivariate nor...

In this paper by using rgα−open sets I define almost rgα−normality and mild rgα−normality also we continue the study of further properties of rgα−normality. We show that these three axioms are regular open hereditary. I also define the class of almost rgα−irresolute mappings and show that rgα−normality is invariant under almost rgα−irresolute M-rgα−open continuous surjection.