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Following our previous work on copula-based nonsymmetric dependence measures, we introduce similar measures for discrete random variables. The measures cover the range between two extremes: independence and complete dependence, which take…
Testing for pairwise independence for the case where the number of variables may be of the same size or even larger than the sample size has received increasing attention in the recent years. We contribute to this branch of the literature…
After variable selection, standard inferential procedures for regression parameters may not be uniformly valid; there is no finite-sample size at which a standard test is guaranteed to approximately attain its nominal size. This problem is…
We derive a compatible discretization method that relies heavily on the underlying geometric structure, and obeys the topological sequences and commuting properties that are constructed. As a sample problem we consider the…
Based on recent progress in research on copula based dependence measures, we review the original Renyi's axioms on symmetric measures and propose a new set of axioms that applies to nonsymmetric measures. We show that nonsymmetric measures…
Although there is an extensive literature on the eigenvalues of high-dimensional sample covariance matrices, much of it is specialized to independent components (IC) models -- in which observations are represented as linear transformations…
We consider the problem of recovering conditional independence relationships between $p$ jointly distributed Hilbertian random elements given $n$ realizations thereof. We operate in the sparse high-dimensional regime, where $n \ll p$ and no…
We discretize a risk-neutral optimal control problem governed by a linear elliptic partial differential equation with random inputs using a Monte Carlo sample-based approximation and a finite element discretization, yielding finite…
This article concerns tests for location parameters in cases where the data dimension is larger than the sample size. We propose a family of tests based on the optimality arguments in Le Cam (1986) under elliptical symmetric. The asymptotic…
In repeated Measure Designs with multiple groups, the primary purpose is to compare different groups in various aspects. For several reasons, the number of measurements and therefore the dimension of the observation vectors can depend on…
This article proposes a class of goodness-of-fit tests for the autocorrelation function of a time series process, including those exhibiting long-range dependence. Test statistics for composite hypotheses are functionals of a (approximated)…
We derive so-called weak and strong \textit{max-laws of large numbers} for $% \max_{1\leq i\leq k_{n}}|1/n\sum_{t=1}^{n}x_{i,n,t}|$ for zero mean stochastic triangular arrays $\{x_{i,n,t}$ $:$ $1$ $\leq $ $t$ $\leq n\}_{n\geq 1}$, with…
Testing procedures for assessing a parametric regression model with circular response and $\mathbb{R}^d$-valued covariate are proposed and analyzed in this work both for independent and for spatially correlated data. The test statistics are…
We study optimal design problems where the design corresponds to a coefficient in the principal part of the state equation. The state equation, in addition, is parameter dependent, and we allow it to change type in the limit of this…
This paper introduces diagnostic tests for the nature of lack of fit in ordinary differential equation models (ODEs) proposed for data. We present a hierarchy of three possible sources of lack of fit: unaccounted-for stochastic variation,…
Measuring dependence between random variables is a fundamental problem in Statistics, with applications across diverse fields. While classical measures such as Pearson's correlation have been widely used for over a century, they have…
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…
We propose an empirical likelihood test that is able to test the goodness of fit of a class of parametric and semi-parametric multiresponse regression models. The class includes as special cases fully parametric models; semi-parametric…
A new gradient-based adaptive sampling method is proposed for design of experiments applications which balances space filling, local refinement, and error minimization objectives while reducing reliance on delicate tuning parameters. High…
This work builds a unified framework for the study of quadratic form distance measures as they are used in assessing the goodness of fit of models. Many important procedures have this structure, but the theory for these methods is dispersed…