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We develope the framework of transitional conditional independence. For this we introduce transition probability spaces and transitional random variables. These constructions will generalize, strengthen and unify previous notions of…
We consider the problem of distribution-free predictive inference, with the goal of producing predictive coverage guarantees that hold conditionally rather than marginally. Existing methods such as conformal prediction offer marginal…
In many applications, the probability density function is subject to experimental errors. In this work the continuos dependence of a class of generalized entropies on the experimental errors is studied. This class includes the C. Shannon,…
We prove general de Finetti type theorems for classical and free independence. The de Finetti type theorems work for all non-easy quantum groups, which generalize a recent work of Banica, Curran and Speicher. We determine maximal…
We introduce a new test for conditional independence which is based on what we call the weighted generalised covariance measure (WGCM). It is an extension of the recently introduced generalised covariance measure (GCM). To test the null…
In this paper we propose a Bayesian answer to testing problems when the hypotheses are not well separated. The idea of the method is to study the posterior distribution of a discrepancy measure between the parameter and the model we want to…
Measurements of systems taken along a continuous functional dimension, such as time or space, are ubiquitous in many fields, from the physical and biological sciences to economics and engineering.Such measurements can be viewed as…
The problem of measuring conditional dependence between two random phenomena arises when a third one (a confounder) has a potential influence on the amount of information between them. A typical issue in this challenging problem is the…
Econometric applications with multi-way clustering often feature a small number of effective clusters or heavy-tailed data, making standard cluster-robust and bootstrap inference unreliable in finite samples. In this paper, we develop a…
In this paper we consider the uniformity testing problem for high-dimensional discrete distributions (multinomials) under sparse alternatives. More precisely, we derive sharp detection thresholds for testing, based on $n$ samples, whether a…
In a recent preprint (Mosegaard and Curtis, 2024, arXiv:2411.13570v2) we analyzed the consequences of ignoring the well-known inconsistency of classical conditional probability densities. We explained how this inconsistency, together with…
In this paper we study some asymptotic properties of the kernel conditional quantile estimator with randomly left-truncated data which exhibit some kind of dependence. We extend the result obtained by Lemdani, Ould-Sa\"id and Poulin [16] in…
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…
In this paper, we introduce and develop the concept of conditional quantization for Borel probability measures on $\mathbb{R}^k,$ considering both constrained and unconstrained frameworks. For each setting, we define the associated…
Distinguishing causal connections from correlations is important in many scenarios. However, the presence of unobserved variables, such as the latent confounder, can introduce bias in conditional independence testing commonly employed in…
In this paper we propose several variants to perform the independence test between two random elements based on recurrence rates. We will show how to calculate the test statistic in each one of these cases. From simulations we obtain that…
We consider the problem of distribution-free conditional predictive inference. Prior work has established that achieving exact finite-sample control of conditional coverage without distributional assumptions is impossible, in the sense that…
Measuring conditional dependencies among the variables of a network is of great interest to many disciplines. This paper studies some shortcomings of the existing dependency measures in detecting direct causal influences or their lack of…
In this paper, we consider the problem of testing independence in high-dimensional settings with missing data. Building upon a recently proposed Kendall-based statistic, we introduce two new modifications specifically designed to…
We study the problem of discrete distribution testing in the two-party setting. For example, in the standard closeness testing problem, Alice and Bob each have $t$ samples from, respectively, distributions $a$ and $b$ over $[n]$, and they…