Related papers: Testing for normality in any dimension based on a …
Classical asymptotic theory for statistical inference usually involves calibrating a statistic by fixing the dimension $d$ while letting the sample size $n$ increase to infinity. Recently, much effort has been dedicated towards…
Standard high-dimensional factor models assume that the comovements in a large set of variables could be modeled using a small number of latent factors that affect all variables. In many relevant applications in economics and finance,…
Statistical techniques are used in all branches of science to determine the feasibility of quantitative hypotheses. One of the most basic applications of statistical techniques in comparative analysis is the test of equality of two…
We find conditions which guarantee moment (in)determinacy of powers and products of nonnegative random variables. We establish new and general results which are based either on the rate of growth of the moments of a random variable or on…
We employ a general Monte Carlo method to test composite hypotheses of goodness-of-fit for several popular multivariate models that can accommodate both asymmetry and heavy tails. Specifically, we consider weighted L2-type tests based on a…
This paper adresses the problem of testing for the equality of $k$ probability distributions on Hilbert spaces, with $k\geqslant 2$. We introduce a generalization of the maximum variance discrepancy called multiple maximum variance…
In this article, we propose a class of $L_q$-norm based U-statistics for a family of global testing problems related to high-dimensional data. This includes testing of mean vector and its spatial sign, simultaneous testing of linear model…
Many commonly used test statistics are based on a norm measuring the evidence against the null hypothesis. To understand how the choice of a norm affects power properties of tests in high dimensions, we study the consistency sets of…
We propose a Bayesian test of normality for univariate or multivariate data against alternative nonparametric models characterized by Dirichlet process mixture distributions. The alternative models are based on the principles of embedding…
There exist some testing procedures based on the maximum mean discrepancy (MMD) to address the challenge of model specification. However, they ignore the presence of estimated parameters in the case of composite null hypotheses. In this…
We study the question of testing structured properties (classes) of discrete distributions. Specifically, given sample access to an arbitrary distribution $D$ over $[n]$ and a property $\mathcal{P}$, the goal is to distinguish between…
A novel method is proposed for detecting changes in the covariance structure of moderate dimensional time series. This non-linear test statistic has a number of useful properties. Most importantly, it is independent of the underlying…
In this article, we prove a normality criterion for a family of meromorphic functions having zeros with some multiplicity which involves sharing of a holomorphic function by the members of the family. Our result generalizes Montel's…
In this paper, we treat the problem of testing for normality as a binary classification problem and construct a feedforward neural network that can successfully detect normal distributions by inspecting small samples from them. The…
It has been a long history in testing whether a mean vector with a fixed dimension has a specified value. Some well-known tests include the Hotelling $T^2$-test and the empirical likelihood ratio test proposed by Owen [Biometrika 75 (1988)…
Anomaly detection (AD) is the machine learning task of identifying highly discrepant abnormal samples by solely relying on the consistency of the normal training samples. Under the constraints of a distribution shift, the assumption that…
Functional panels are collections of functional time series, and arise often in the study of high frequency multivariate data. We develop a portmanteau style test to determine if the cross-sections of such a panel are independent and…
In this paper we consider the uniformity testing problem for high-dimensional discrete distributions (multinomials) under sparse alternatives. More precisely, we derive sharp detection thresholds for testing, based on $n$ samples, whether a…
The paper deals with measures of nonlinearity. In state estimation, they are utilized i) to select a suitable state estimation algorithm by assessing the nonlinearity of a system model, ii) to adapt the estimation algorithm structure or…
This paper investigates the problem of testing independence of two random vectors of general dimensions. For this, we give for the first time a distribution-free consistent test. Our approach combines distance covariance with the…