Related papers: Simple sufficient condition for inadmissibility of…

We propose a two-sample test for high-dimensional means that requires neither distributional nor correlational assumptions, besides some weak conditions on the moments and tail properties of the elements in the random vectors. This…

We consider a nonparametric Bayesian approach to estimation and testing for a multivariate monotone density. Instead of following the conventional Bayesian route of putting a prior distribution complying with the monotonicity restriction,…

In two-sampling testing, one observes two independent sequences of independent and identically distributed random variables distributed according to the distributions $P_1$ and $P_2$ and wishes to decide whether $P_1=P_2$ (null hypothesis)…

We study the problem of constructing a probability density in 2N-dimensional phase space which reproduces a given collection of $n$ joint probability distributions as marginals. Only distributions authorized by quantum mechanics, i.e.…

We study a novel class of affine invariant and consistent tests for multivariate normality. The tests are based on a characterization of the standard $d$-variate normal distribution by means of the unique solution of an initial value…

In this paper we propose the use of $\phi$-divergences as test statistics to verify simple hypotheses about a one-dimensional parametric diffusion process $\de X_t = b(X_t, \theta)\de t + \sigma(X_t, \theta)\de W_t$, from discrete…

In this paper, we propose an explicit closed-form Bayes factor for the problem of two-sample hypothesis testing. The proposed approach can be regarded as a Bayesian version of the pooled-variance t-statistic and has various appealing…

This paper considers the problem of testing temporal homogeneity of $p$-dimensional population mean vectors from the repeated measurements of $n$ subjects over $T$ times. To cope with the challenges brought by high-dimensional longitudinal…

Conditional independence (CI) tests underlie many approaches to model testing and structure learning in causal inference. Most existing CI tests for categorical and ordinal data stratify the sample by the conditioning variables, perform…

The statistics and machine learning communities have recently seen a growing interest in classification-based approaches to two-sample testing. The outcome of a classification-based two-sample test remains a rejection decision, which is not…

Let $\mathbf{X} = (X_i)_{1\leq i \leq n}$ be an i.i.d. sample of square-integrable variables in $\mathbb{R}^d$, \GB{with common expectation $\mu$ and covariance matrix $\Sigma$, both unknown.} We consider the problem of testing if $\mu$ is…

Employing Hilbert-Schmidt measure, we explicitly compute and analyze a number of determinantal product (bivariate) moments |rho|^k |rho^{PT}|^n, k,n=0,1,2,3,..., PT denoting partial transpose, for both generic (9-dimensional) two-rebit…

We develop a new permutation test for inference on a subvector of coefficients in linear models. The test is exact when the regressors and the error terms are independent. Then, we show that the test is asymptotically of correct level,…

Asymptotic methods for hypothesis testing in high-dimensional data usually require the dimension of the observations to increase to infinity, often with an additional condition on its rate of increase compared to the sample size. On the…

Let $X$ be an observable random variable with unknown distribution function $F(x) = \mathbb{P}(X \leq x), - \infty < x < \infty$, and let \[\ \theta = \sup\left \{ r \geq 0:~ \mathbb{E}|X|^{r} < \infty \right \}. \] We call $\theta$ the…

In this paper we consider the two-type Moran model with $N$ individuals. Each individual is assigned a resampling rate, drawn independently from a probability distribution ${\mathbb P}$ on ${\mathbb R}_+$, and a type, either $1$ or $0$.…

The likelihood ratio statistic, with its asymptotic $\chi^2$ distribution at regular model points, is often used for hypothesis testing. At model singularities and boundaries, however, the asymptotic distribution may not be $\chi^2$, as…

Symmetry plays a central role in the sciences, machine learning, and statistics. For situations in which data are known to obey a symmetry, a multitude of methods that exploit symmetry have been developed. Statistical tests for the presence…

Meta-analysis combines results from multiple studies aiming to increase power in finding their common effect. It would typically reject the null hypothesis of no effect if any one of the studies shows strong significance. The partial…

We address the problem of producing a lower bound for the mean of a discrete probability distribution, with known support over a finite set of real numbers, from an iid sample of that distribution. Up to a constant, this is equivalent to…