Related papers: On the surjectivity of the conditional expectation…

Exogenous heterogeneity, for example, in the form of instrumental variables can help us learn a system's underlying causal structure and predict the outcome of unseen intervention experiments. In this paper, we consider linear models in…

Theoretically, the conditional expectation of a square-integrable random variable $Y$ given a $d$-dimensional random vector $X$ can be obtained by minimizing the mean squared distance between $Y$ and $f(X)$ over all Borel measurable…

We propose a new method to test conditional independence of two real random variables $Y$ and $Z$ conditionally on an arbitrary third random variable $X$. %with $F_{.|.}$ representing conditional distribution functions, The partial copula…

Researchers regularly perform conditional prediction using imputed values of missing data. However, applications of imputation often lack a firm foundation in statistical theory. This paper originated when we were unable to find analysis…

A general setting for nested subdivisions of a bounded real set into intervals defining the digits $X_1,X_2,...$ of a random variable $X$ with a probability density function $f$ is considered. Under the weak condition that $f$ is almost…

Regressing a function $F$ on $\mathbb{R}^d$ without the statistical and computational curse of dimensionality requires special statistical models, for example that impose geometric assumptions on the distribution of the data (e.g., that its…

The need to condition distributional properties such as expectation, variance, and entropy arises in algorithmic fairness, model simplification, robustness and many other areas. At face value however, distributional properties are not…

This article addresses the problem of testing the conditional independence of two generic random vectors $X$ and $Y$ given a third random vector $Z$, which plays an important role in statistical and machine learning applications. We propose…

Let G be a connected reductive group defined over a non-archimedean local field of characteristic 0. We assume G is quasi-split, adjoint and absolutly simple. Let g be the Lie algebra of G. We consider the space of the invariant…

Many key quantities in statistics and probability theory such as the expectation, quantiles, expectiles and many risk measures are law-determined maps from a space of random variables to the reals. We call such a law-determined map, which…

Let $X\in \mathbb{R}^p$ and $Y\in \mathbb{R}$ be two random variables. We estimate the conditional covariance matrix $\mathrm{Cov}\left(\mathrm{E}\left[\boldsymbol{X}\vert Y\right]\right)$ applying a plug-in kernel-based algorithm to its…

Conditional independence in a multivariate normal (or Gaussian) distribution is characterized by the vanishing of subdeterminants of the distribution's covariance matrix. Gaussian conditional independence models thus correspond to algebraic…

We present a general nonparametric approach for testing whether a statistical parameter defined through conditional distributions is constant across the conditioning variables. Such hypotheses arise naturally in problems such as assessing…

We revisit the problem of condensation for independent, identically distributed random variables with a power-law tail, conditioned by the value of their sum. For large values of the sum, and for a large number of summands, a condensation…

In this paper, we obtain a comparison theorem and a invariant representation theorem for backward stochastic differential equations (BSDEs) without any assumption on the second variable $z$. Using the two results, we further develop the…

We give a finite-sample analysis of predictive inference procedures after model selection in regression with random design. The analysis is focused on a statistically challenging scenario where the number of potentially important…

We study probabilistically informative (weak) versions of transitivity, by using suitable definitions of defaults and negated defaults, in the setting of coherence and imprecise probabilities. We represent p-consistent sequences of defaults…

For a linear combination of random variables, fix some confidence level and consider the quantile of the combination at this level. We are interested in the partial derivatives of the quantile with respect to the weights of the random…

The Gumbel-Softmax probability distribution allows learning discrete tokens in generative learning, while the Gumbel-Argmax probability distribution is useful in learning discrete structures in discriminative learning. Despite the efforts…

Multivariate extreme value theory assumes a multivariate domain of attraction condition for the distribution of a random vector. This necessitates that each component satisfies a marginal domain of attraction condition. An approximation of…