Related papers: Conditional independence relations and log-linear …
Random permutations with distribution conditionally uniform given the set of record values can be generated in a unified way, coherently for all values of $n$. Our central example is a two-parameter family of random permutations that are…
We consider the structural change in a class of discrete valued time series that the conditional distribution follows a one-parameter exponential family. We propose a change-point test based on the maximum likelihood estimator of the…
We study a family of determinantal ideals whose decompositions encode the structural zeros in conditional independence models with hidden variables. We provide explicit decompositions of these ideals and, for certain subclasses of models,…
Many high-dimensional hypothesis tests aim to globally examine marginal or low-dimensional features of a high-dimensional joint distribution, such as testing of mean vectors, covariance matrices and regression coefficients. This paper…
Relational models for contingency tables are generalizations of log-linear models, allowing effects associated with arbitrary subsets of cells in a possibly incomplete table, and not necessarily containing the overall effect. In this…
We propose a sequential, anytime-valid method to test the conditional independence of a response $Y$ and a predictor $X$ given a random vector $Z$. The proposed test is based on e-statistics and test martingales, which generalize likelihood…
Learning causal relations from observational data is a fundamental problem with wide-ranging applications across many fields. Constraint-based methods infer the underlying causal structure by performing conditional independence tests.…
It is well known that conditional independence can be used to factorize a joint probability into a multiplication of conditional probabilities. This paper proposes a constructive definition of inter-causal independence, which can be used to…
Dynamic logit models are popular tools in economics to measure state dependence. This paper introduces a new method to derive moment restrictions in a large class of such models with strictly exogenous regressors and fixed effects. We…
In this paper, we address the problem of testing independence between two high-dimensional random vectors. Our approach involves a series of max-sum tests based on three well-known classes of rank-based correlations. These correlation…
Empirical processes for stationary, causal sequences are considered. We establish empirical central limit theorems for classes of indicators of left half lines, absolutely continuous functions and piecewise differentiable functions. Sample…
We propose a method to construct a joint statistical model for mixed-domain data to analyze their dependence. Multivariate Gaussian and log-linear models are particular examples of the proposed model. It is shown that the functional…
Association between categorical variables in contingency tables is analyzed using the information identities based on multivariate multinomial distributions. A scheme of geometric decompositions of the information identities is developed to…
This paper addresses two central problems for probabilistic processing models: parameter estimation from incomplete data and efficient retrieval of most probable analyses. These questions have been answered satisfactorily only for…
We introduce the notion of a conditionally free product and conditionally free convolution. We describe this convolution both from a combinatorial point of view, by showing its connection with the lattice of non-crossing partitions, and…
We study hidden-variable models from quantum mechanics, and their abstractions in purely probabilistic and relational frameworks, by means of logics of dependence and independence, based on team semantics. We show that common desirable…
Likelihood-free inference is concerned with the estimation of the parameters of a non-differentiable stochastic simulator that best reproduce real observations. In the absence of a likelihood function, most of the existing inference methods…
A notion of conditionally identically distributed (c.i.d.) sequences has been studied as a form of stochastic dependence that is weaker than exchangeability, but is equivalent to exchangeability for stationary sequences. In this article we…
One of the most popular class of tests for independence between two random variables is the general class of rank statistics which are invariant under permutations. This class contains Spearman's coefficient of rank correlation statistic,…
We discuss a general method to construct correlated binomial distributions by imposing several consistent relations on the joint probability function. We obtain self-consistency relations for the conditional correlations and conditional…