统计理论
We consider the problem of constructing a global, probabilistic, and non-asymptotic confidence region for an unknown function observed on a random design. The unknown function is assumed to lie in a reproducing kernel Hilbert space (RKHS).…
Over the last years, there has been a significant amount of work studying the power of specific classes of computationally efficient estimators for multiple statistical parametric estimation tasks, including the estimators classes of…
Recursive max-linear vectors provide models for causal dependence between large values of random variables that are supported on directed acyclic graphs, but the standard assumption that all nodes of such a graph are observed can be…
A celebrated result of Pollard proves asymptotic consistency for $k$-means clustering when the population distribution has finite variance. In this work, we point out that the population-level $k$-means clustering problem is, in fact,…
This paper deals with the process $X = (X_t)_{t\in [0,T]}$ defined by the stochastic differential equation (SDE) $dX_t = (a(X_t) + b(Y_t))dt +\sigma(X_t)dW_1(t)$, where $W_1$ is a Brownian motion and $Y$ is an exogenous process. The first…
Maximum likelihood estimators for time-dependent mean functions within Gaussian processes are provided in the context of continuous observations. We find the widest possible class of mean functions for which the likelihood function can be…
Basu's via media is what he referred to as the middle road between the Bayesian and frequentist poles. He seemed skeptical that a suitable via media could be found, but I disagree. My basic claim is that the likelihood alone can't reliably…
High-dimensional linear models have been widely studied, but the developments in high-dimensional generalized linear models, or GLMs, have been slower. In this paper, we propose an empirical or data-driven prior leading to an empirical…
We develop methodology and theory for the detection of a phase transition in a time-series of high-dimensional random matrices. In the model we study, at each time point \( t = 1,2,\ldots \), we observe a deformed Wigner matrix \(…
We establish minimax convergence rates for score-based generative models (SGMs) under the $1$-Wasserstein distance. Assuming the target density $p^\star$ lies in a nonparametric $\beta$-smooth H\"older class with either compact support or…
Minimum divergence estimators provide a natural choice of estimators in a statistical inference problem. Different properties of various families of these divergence measures such as Hellinger distance, power divergence, density power…
We consider the problem of estimating `preference' or `strength' parameters in three-way comparison experiments, each composed of a series of paired comparisons, but where only the single `preferred' or `strongest' candidate is known in…
In this paper, the asymptotic theory presented in (Caponera et al., 2022) for spline-type anysotropic covariance estimator on the 2-dimensional sphere is generalized to the case of connected and compact two-point homogeneous spaces.
We give some results relating asymptotic characterisations of maximum entropy probability measures to characterisations of Bayes optimal classifiers. Our main theorems show that maximum entropy is a universally Bayes optimal decision rule…
Spectral properties of random matrices play an important role in statistics, machine learning, communications, and many other areas. Engaging results regarding the convergence of the empirical spectral distribution (ESD) and the…
Local Fr'echet Regression (LFR) is a nonparametric regression method for settings in which the explanatory variable lies in a Euclidean space and the response variable lies in a metric space. It is used to estimate smooth trajectories in…
In copula modeling, the simplifying assumption has recently been the object of much interest. Although it is very useful to reduce the computational burden, it remains far from obvious whether it is actually satisfied in practice. We…
In this paper, we develop category theory of Markov kernels to study categorical aspects of Bayesian inversions. As a result, we present a unified model for Bayesian supervised learning, encompassing Bayesian density estimation. We…
The problem of estimating, from a random sample of points, the dimension of a compact subset $S$ of the Euclidean space is considered. The emphasis is put on consistency results in the statistical sense. That is, statements of convergence…
We say that a matrix $P$ with non-negative entries majorizes another such matrix $Q$ if there is a stochastic matrix $T$ such that $Q=TP$. We study matrix majorization in large samples and in the catalytic regime in the case where the…