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We obtain an exact necessary and sufficient condition for the existence and uniqueness of equilibrium asset prices in infinite horizon, discrete-time, arbitrage free environments. Through several applications we show how the condition…
Conditional independence (CI) testing arises naturally in many scientific problems and applications domains. The goal of this problem is to investigate the conditional independence between a response variable $Y$ and another variable $X$,…
Bivariate count data arise in several different disciplines (epidemiology, marketing, sports statistics, etc., to name but a few) and the bivariate Poisson distribution which is a generalization of the Poisson distribution plays an…
We prove large and moderate deviation principles for the distribution of an empirical mean conditioned by the value of the sum of discrete i.i.d. random variables. Some applications for combinatoric problems are discussed.
Motivated by applications in biological science, we propose a novel test to assess the conditional mean dependence of a response variable on a large number of covariates. Our procedure is built on the martingale difference divergence…
We establish a general concentration result for the 1-Wasserstein distance between the empirical measure of a sequence of random variables and its expectation. Unlike standard results that rely on independence (e.g., Sanov's theorem) or…
By the Lindeberg-L\'evy central limit theorem, standardized partial sums of a sequence of mutually independent and identically distributed random variables converge in law to the standard normal distribution. It is known that mutual…
In this article, we consider the problem of simultaneous testing of hypotheses when the individual test statistics are not necessarily independent. Specifically, we consider the problem of simultaneous testing of point null hypotheses…
The aim of this thesis is to find a solution to the non-parametric independence problem in separable metric spaces. Suppose we are given finite collection of samples from an i.i.d. sequence of paired random elements, where each marginal has…
We study a class of conditional independence models for discrete data with the property that one or more log-linear interactions are defined within two different marginal distributions and then constrained to 0; all the conditional…
We provide a method to construct entanglement criteria for arbitrary multipartite systems of discrete or continuous variables and hybrid combinations of both. While any set of local operators generates a sufficient condition for…
(To appear in The American Statistician.) Distance covariance (Sz\'ekely, Rizzo, and Bakirov, 2007) is a fascinating recent notion, which is popular as a test for dependence of any type between random variables $X$ and $Y$. This approach…
We consider joint inversion for two or more unknown parameters from observational data in the Bayesian framework. Standard approaches often either treat the parameters as independent or impose structural similarity through regularisation…
Conducting valid statistical analyses is challenging in the presence of missing-not-at-random (MNAR) data, where the missingness mechanism is dependent on the missing values themselves even conditioned on the observed data. Here, we…
We study stochastic choice across decision problems, each represented as a menu of action labels paired with observable outcome vectors. We propose a consistency condition for behavior in decision problems composed of two separable…
Fields like public health, public policy, and social science often want to quantify the degree of dependence between variables whose relationships take on unknown functional forms. Typically, in fact, researchers in these fields are…
Testing hypothesis of independence between two random elements on a joint alphabet is a fundamental exercise in statistics. Pearson's chi-squared test is an effective test for such a situation when the contingency table is relatively small.…
Let $\mathbf{X}(n) \in \mathbb{R}^d$ be a sequence of random vectors, where $n\in\mathbb{N}$ and $d = d(n)$. Under certain weakly dependence conditions, we prove that the distribution of the maximal component of $\mathbf{X}$ and the…
Possibilistic conditional independence is investigated: we propose a definition of this notion similar to the one used in probability theory. The links between independence and non-interactivity are investigated, and properties of these…
A general separability condition on the second moment (covariance matrix) for continuous variable two-party systems is derived by an analysis analogous to the derivation of the Kennard's uncertainty relation without referring to the…