统计理论

Estimating optimal transport maps between two distributions from respective samples is an important element for many machine learning methods. To do so, rather than extending discrete transport maps, it has been shown that estimating the…

We establish the consistency of classical scaling under a broad class of noise models, encompassing many commonly studied cases in literature. Our approach requires only finite fourth moments of the noise, significantly weakening standard…

Fractional cumulative residual entropy (FCRE) is a powerful tool for the analysis of complex systems. Most of the theoretical results and applications related to the FCRE of the lifetime random variable are based on the distribution…

This article considers the automatic selection problem of the relevant explanatory variables in a right-censored model on a massive database. We propose and study four aggregated censored adaptive LASSO estimators constructed by dividing…

Multi-stream sequential change detection involves simultaneously monitoring many streams of data and trying to detect when their distributions change, if at all. Here, we theoretically study multiple testing issues that arise from detecting…

Deep Gaussian processes have recently been proposed as natural objects to fit, similarly to deep neural networks, possibly complex features present in modern data samples, such as compositional structures. Adopting a Bayesian nonparametric…

We consider testing a composite null hypothesis $\mathcal{P}$ against a point alternative $\mathsf{Q}$ using e-variables, which are nonnegative random variables $X$ such that $\mathbb{E}_\mathsf{P}[X] \leq 1$ for every $\mathsf{P} \in…

The spectral density matrix is a fundamental object of interest in time series analysis, and it encodes both contemporary and dynamic linear relationships between component processes of the multivariate system. In this paper we develop…

We study the flexible piecewise exponential model in a high dimensional setting where the number of covariates $p$ grows proportionally to the number of observations $n$ and under the hypothesis of random uncorrelated Gaussian designs. We…

In a regression setting with a response vector and given regressor vectors, a typical question is to what extent the response is related to these regressors, specifically, how well it can be approximated by a linear combination of the…

To perform regression analysis in high dimensions, lasso or ridge estimation are a common choice. However, it has been shown that these methods are not robust to outliers. Therefore, alternatives as penalized M-estimation or the sparse…

We introduce the concept of shape-regular regression maps as a framework to derive optimal rates of convergence for various non-parametric local regression estimators. Using Vapnik-Chervonenkis theory, we establish upper and lower bounds on…

We introduce two uncertainty measures, say weighted past varentropy (WPVE) and weighted paired dynamic varentropy (WPDVE). Several properties of these proposed measures, including their effect under the monotone transformations are studied.…

Online A/B testing is widely used in the internet industry to inform decisions on new feature roll-outs. For online marketplaces (such as advertising markets), standard approaches to A/B testing may lead to biased results when buyers…

Consider bivariate observations $(X_1,Y_1), \ldots, (X_n,Y_n) \in \mathbb{R}\times \mathbb{R}$ with unknown conditional distributions $Q_x$ of $Y$, given that $X = x$. The goal is to estimate these distributions under the sole assumption…

Pursuing invariant prediction from heterogeneous environments opens the door to learning causality in a purely data-driven way and has several applications in causal discovery and robust transfer learning. However, existing methods such as…

In this article, we develop a new class of multivariate distributions adapted for count data, called Tree P\'olya Splitting. This class results from the combination of a univariate distribution and singular multivariate distributions along…

The double Heston model is one of the most popular option pricing models in financial theory. It is applied to several issues such that risk management and volatility surface calibration. This paper deals with the problem of global…

Statistical inference for stochastic processes has advanced significantly due to applications in diverse fields, but challenges remain in high-dimensional settings where parameters are allowed to grow with the sample size. This paper…

Ancestral inference for branching processes in random environments involves determining the ancestor distribution parameters using the population sizes of descendant generations. In this paper, we introduce a new methodology for ancestral…