相关论文: Skewness and kurtosis as locally best invariant te…

Judging the significance and reproducibility of quantitative research requires a good understanding of relevant uncertainties, but it is often unclear how well these have been evaluated and what they imply. Reported scientific uncertainties…

In this paper we provide the asymptotic theory of the general of $\phi$-divergences measures, which includes the most common divergence measures : Renyi and Tsallis families and the Kullback-Leibler measure. Instead of using the Parzen…

Testing the equality of the covariance matrices of two high-dimensional samples is a fundamental inference problem in statistics. Several tests have been proposed but they are either too liberal or too conservative when the required…

In this paper we consider germs of smooth Levi flat hypersurfaces, under the following notion of local equivalence: S_1 ~ S_2 if their one-sided neighborhoods admit a biholomorphism smooth up to the boundary. We introduce a simple invariant…

There is an increasing interest in algorithms to learn invariant correlations across training environments. A big share of the current proposals find theoretical support in the causality literature but, how useful are they in practice? The…

It is well-known that observing nonlocal correlations allows us to draw conclusions about the quantum systems under consideration. In some cases this yields a characterisation which is essentially complete, a phenomenon known as…

The task of binary quantum hypothesis testing is to determine the state of a quantum system via measurements on it, given the side information that it is in one of two possible states, say $\rho$ and $\sigma$. This task is generally studied…

Black box variational inference (BBVI) with reparameterization gradients triggered the exploration of divergence measures other than the Kullback-Leibler (KL) divergence, such as alpha divergences. In this paper, we view BBVI with…

We show posterior convergence for the community structure in the planted bi-section model, for several interesting priors. Examples include where the label on each vertex is iid Bernoulli distributed, with some parameter $r\in(0,1)$. The…

Under a multinormal distribution with an arbitrary unknown covariance matrix, the main purpose of this paper is to propose a framework to achieve the goal of reconciliation of Bayesian, frequentist, and Fisher's reporting $p$-values,…

Local unitary invariants allow one to test whether multipartite states are equivalent up to local basis changes. Equivalently, they specify the geometry of the "orbit space" obtained by factoring out local unitary action from the state…

Principled nonparametric tests for regression curvature in $\mathbb{R}^{d}$ are often statistically and computationally challenging. This paper introduces the stratified incomplete local simplex (SILS) tests for joint concavity of…

We propose a new probabilistic characterization of the uniform distribution on the hypersphere in terms of the distribution of pairwise inner products, extending the ideas of \citep{cuesta2009projection,cuesta2007sharp} in a data-driven…

The classical binary hypothesis testing problem is revisited. We notice that when one of the hypotheses is composite, there is an inherent difficulty in defining an optimality criterion that is both informative and well-justified. For…

We discuss a family of time-reversible, scale-invariant diffusions with singular coefficients. In analogy with the standard Gaussian theory, a corresponding family of generalized characteristic functions provides a useful tool for proving…

The asymptotic expansion of the distribution of the gradient test statistic is derived for a composite hypothesis under a sequence of Pitman alternative hypotheses converging to the null hypothesis at rate $n^{-1/2}$, $n$ being the sample…

We consider goodness-of-fit tests with i.i.d. samples generated from a categorical distribution $(p_1,...,p_k)$. For a given $(q_1,...,q_k)$, we test the null hypothesis whether $p_j=q_{\pi(j)}$ for some label permutation $\pi$. The…

The family of multivariate skew-normal distributions has many interesting properties. It is shown here that these hold for a general class of skew-elliptical distributions. For this class, several stochastic representations are established…

Given observations from a circular random variable contaminated by an additive measurement error, we consider the problem of minimax optimal goodness-of-fit testing in a non-asymptotic framework. We propose direct and indirect testing…

Discrete normal distributions are defined as the distributions with prescribed means and covariance matrices which maximize entropy on the integer lattice support. The set of discrete normal distributions form an exponential family with…