统计理论

Prediction sets based on full conformal prediction have seen an increasing interest in statistical learning due to their universal marginal coverage guarantees. However, practitioners have refrained from using it in applications for two…

This paper considers generalizations of the functional equations that characterize the lack-of-memory properties at univariate and bivariate levels. Specifically, we extend the univariate functional equation introduced by Kaminsky (1983)…

The objective of this paper is to establish a general asymptotic representation (\textit{GAR}) for a wide range of statistics, employing two fundamental processes: the functional empirical process (\textit{fep}) and the residual functional…

It is commonly accepted that some phenomena are social: for example, individuals' smoking habits often correlate with those of their peers. Such correlations can have a variety of explanations, such as direct contagion or shared…

This paper examines the construction of confidence sets for parameters defined as linear functionals of a function of W and X whose conditional mean given Z and X equals the conditional mean of another variable Y given Z and X. Many…

The rating of items based on pairwise comparisons has been a topic of statistical investigation for many decades. Numerous approaches have been proposed. One of the best known is the Bradley-Terry model. This paper seeks to assemble and…

We develop a class of non-Gaussian translation processes that extend classical stochastic differential equations (SDEs) by prescribing arbitrary absolutely continuous marginal distributions. Our approach uses a copula-based transformation…

This paper studies the problems of identifiability and estimation in high-dimensional nonparametric latent structure models. We introduce an identifiability theorem that generalizes existing conditions, establishing a unified framework…

We consider nonlinear mixed effects models including high-dimensional covariates to model individual parameters variability. The objective is to identify relevant covariates among a large set under sparsity assumption and to estimate model…

We consider a joint survival and mixed-effects model to explain the survival time from longitudinal data and high-dimensional covariates in a population. The longitudinal data is modeled using a non linear mixed-effects model to account for…

Variational Bayes (VB) provides a computationally efficient alternative to Markov Chain Monte Carlo, especially for high-dimensional and large-scale inference. However, existing theory on VB primarily focuses on fixed-dimensional settings…

An algebraic set is defined as the zero locus of a system of real polynomial equations. In this paper we address the problem of recovering an unknown algebraic set $\mathcal{A}$ from noisy observations of latent points lying on…

We argue that the Bayesian paradigm, of a prior which represents the beliefs of the statistician before observing the data, is not feasible in ultra-high-dimensional models. We claim that natural priors that represent the a priori beliefs…

Parameter estimation is a fundamental problem in science and engineering. In many safety-critical applications, one is not only interested in a {\it point} estimator, but also the uncertainty bound that can self-assess the accuracy of the…

We derive tractable criteria for the consistency of Bayesian tree reconstruction procedures, which constitute a central class of algorithms for inferring common ancestry among DNA sequence samples in phylogenetics. Our results encompass…

We consider the problem of learning the underlying causal structure among a set of variables, which are assumed to follow a Bayesian network or, more specifically, a linear recursive structural equation model (SEM) with the associated…

We develop a theory for functional independent component analysis in an infinite-dimensional framework using Sobolev spaces that accommodate smoother functions. The notion of penalized kurtosis is introduced motivated by Silverman's method…

Many machine learning and optimization algorithms are built upon the framework of stochastic approximation (SA), for which the selection of step-size (or learning rate) $\{\alpha_n\}$ is crucial for success. An essential condition for…

In this paper we consider a dynamic Erd\H{o}s-R\'enyi graph in which edges, according to an alternating renewal process, change from present to absent and vice versa. The objective is to estimate the on- and off-time distributions while…

This paper studies distribution-free inference in settings where the data set has a hierarchical structure -- for example, groups of observations, or repeated measurements. In such settings, standard notions of exchangeability may not hold.…