Related papers: One- and two-sample nonparametric tests for the si…
The two-sample test is a fundamental problem in statistics with a wide range of applications. In the realm of high-dimensional data, nonparametric methods have gained prominence due to their flexibility and minimal distributional…
Hierarchically-organized data arise naturally in many psychology and neuroscience studies. As the standard assumption of independent and identically distributed samples does not hold for such data, two important problems are to accurately…
We consider the problem of detecting the presence of a spatially correlated multichannel signal corrupted by additive Gaussian noise (i.i.d across sensors). No prior knowledge is assumed about the system parameters such as the noise…
This paper describes an R package implementing large sample tests and confidence intervals (based on the central limit theorem) for various parameters. The one and two sample mean and variance contexts are considered. The statistics for all…
Given independent samples from two univariate distributions, the one-sided Wilcoxon-Mann-Whitney statistic may be used to conduct a rank-based test of first-order stochastic dominance. We broaden the scope of applicability of such tests by…
We introduce two novel non-parametric statistical hypothesis tests. The first test, called the relative test of dependency, enables us to determine whether one source variable is significantly more dependent on a first target variable or a…
Two-sample inference for the difference of population means typically relies upon a Central Limit Theorem approximation. When data are drawn from a Negative Binomial distribution, previous work of Shilane et al. (2010) showed that a Normal…
Assessing agreement between two instruments is crucial in clinical studies to evaluate the similarity between two methods measuring the same subjects. This paper introduces a novel coefficient, termed rho1, to measure agreement between…
In 1948, W. Hoeffding introduced a large class of unbiased estimators called U-statistics, defined as the average value of a real-valued m-variate function h calculated at all possible sets of m points from a random sample. In the present…
Hoeffding's U-statistics model combinatorial-type matrix parameters (appearing in CS theory) in a natural way. This paper proposes using these statistics for analyzing random compressed sensing matrices, in the non-asymptotic regime…
The comparison of a parameter in $k$ populations is a classical problem in statistics. Testing for the equality of means or variances are typical examples. Most procedures designed to deal with this problem assume that $k$ is fixed and that…
Standard inference about a scalar parameter estimated via GMM amounts to applying a t-test to a particular set of observations. If the number of observations is not very large, then moderately heavy tails can lead to poor behavior of the…
The notion of a $U$-statistic for an $n$-tuple of identical quantum systems is introduced in analogy to the classical (commutative) case: given a selfadjoint `kernel' $K$ acting on $(\mathbb{C}^{d})^{\otimes r}$ with $r<n$, we define the…
Inference based on the penalized density ratio model is proposed and studied. The model under consideration is specified by assuming that the log--likelihood function of two unknown densities is of some parametric form. The model has been…
Mendelian randomization (MR) has been a popular method in genetic epidemiology to estimate the effect of an exposure on an outcome using genetic variants as instrumental variables (IV), with two-sample summary-data MR being the most…
As the most important tool to provide high-level evidence-based medicine, researchers can statistically summarize and combine data from multiple studies by conducting meta-analysis. In meta-analysis, mean differences are frequently used…
In this paper we propose new smoothed sign and Wilcoxon's signed rank tests, which are based on a kernel estimator of the underlying distribution function of data. We discuss approximations of $p$-values and asymptotic properties of these…
The distribution function of a random distance in three dimensions is given and some new three-dimensional d2-tests of randomness are suggested. We show that our test statistics are not correlated with the usual test statistics and are…
This paper contains sharp estimates about the distribution of multiple random integrals of functions of several variables with respect to a normalized empirical measure, about the distribution of U-statistics and multiple Wiener-Ito…
We combine an axiomatics of R\'{e}nyi with the $q$--deformed version of Khinchin axioms to obtain a measure of information (i.e., entropy) which accounts both for systems with embedded self-similarity and non-extensivity. We show that the…