统计理论

We study the variational inference problem of minimizing a regularized R\'enyi divergence over an exponential family. We propose to solve this problem with a Bregman proximal gradient algorithm. We propose a sampling-based algorithm to…

Chatterjee's correlation coefficient has recently been proposed as a new association measure for bivariate random vectors that satisfies a number of desirable properties. Among these properties is the feature that the coefficient equals one…

The H\"usler-Reiss distribution describes the limit of the pointwise maxima of a bivariate normal distribution. This distribution is defined by a single parameter, $\lambda$. We provide asymptotic theory for maximum likelihood estimation of…

This paper investigates a partially linear spatial autoregressive panel data model that incorporates fixed effects, constant and time-varying regression coefficients, and a time-varying spatial lag coefficient. A two-stage least squares…

We investigate the theoretical performances of the Partial Least Square (PLS) algorithm in a high dimensional context. We provide upper bounds on the risk in prediction for the statistical linear model when considering the PLS estimator.…

Given independent random variables $Y_1, \ldots, Y_n$ with $Y_i \in \{0,1\}$ we test the hypothesis whether the underlying success probabilities $p_i$ are constant or whether they are periodic with an unspecified period length of $r \ge 2$.…

Let $X=(X_1,\ldots,X_p)$ be a $p$-variate random vector and $F$ a fixed finite set. In a number of applications, mainly in genetics, it turns out that $X_i\in F$ for each $i=1,\ldots,p$. Despite the latter fact, to obtain a knockoff…

We provide a novel dimension-free uniform concentration bound for the empirical risk function of constrained logistic regression. Our bound yields a milder sufficient condition for a uniform law of large numbers than conditions derived by…

Kernel techniques are among the most influential approaches in data science and statistics. Under mild conditions, the reproducing kernel Hilbert space associated to a kernel is capable of encoding the independence of $M\ge 2$ random…

Major progress has been made in the previous decade to characterize the asymptotic behavior of regularized M-estimators in high-dimensional regression problems in the proportional asymptotic regime where the sample size $n$ and the number…

We theoretically analyze the properties of a geodesic random walk on the Euclidean $d$-sphere. Specifically, we prove that the random walk's transition kernel is Wasserstein contractive with a contraction rate which can be bounded from…

In this article, we study the test for independence of two random elements $X$ and $Y$ lying in an infinite dimensional space ${\cal{H}}$ (specifically, a real separable Hilbert space equipped with the inner product $\langle .,…

Multivariate adaptive regression splines (MARS) is a popular method for nonparametric regression introduced by Friedman in 1991. MARS fits simple nonlinear and non-additive functions to regression data. We propose and study a natural lasso…

Supervised learning with missing data aims at building the best prediction of a target output based on partially-observed inputs. Major approaches to address this problem can be decomposed into $(i)$ impute-then-predict strategies, which…

The consistency of the maximum likelihood estimator for mixtures of elliptically-symmetric distributions for estimating its population version is shown, where the underlying distribution $P$ is nonparametric and does not necessarily belong…

The topic of robustness is experiencing a resurgence of interest in the statistical and machine learning communities. In particular, robust algorithms making use of the so-called median of means estimator were shown to satisfy strong…

We consider the problem of constructing multiple independent conditional randomization tests using a single dataset. Because the tests are independent, the randomization p-values can be interpreted individually and combined using standard…

Linear regression is arguably the most widely used statistical method. With fixed regressors and correlated errors, the conventional wisdom is to modify the variance-covariance estimator to accommodate the known correlation structure of the…

We consider the problem of estimating an unknown parameter vector ${\boldsymbol \theta}\in{\mathbb R}^n$, given noisy observations ${\boldsymbol Y} = {\boldsymbol \theta}{\boldsymbol \theta}^{\top}/\sqrt{n}+{\boldsymbol Z}$ of the rank-one…

In this paper we revisit the likelihood geometry of Gaussian graphical models. We give a detailed proof that the ML-degree behaves monotonically on induced subgraphs. Furthermore, we complete a missing argument that the ML-degree of the…