统计理论

Stochastic comparisons of series and parallel systems are important in many areas of engineering, operations research and reliability analysis. These comparisons allow for the evaluation of the performance and reliability of systems under…

This paper investigates the asymptotic properties of quantile regression estimators in linear models, with a particular focus on polynomial regressors and robustness to heavy-tailed noise. Under independent and identically distributed…

Given a sample $X_0,...,X_{n-1}$ from a $d$-dimensional stationary time series $(X_t)_{t \in \mathbb{Z}}$, the most commonly used estimator for the spectral density matrix $F(\theta)$ at a given frequency $\theta \in [0,2\pi)$ is the…

Many flexible families of positive random variables exhibit non-closed forms of the density and distribution functions and this feature is considered unappealing for modelling purposes. However, such families are often characterized by a…

This note extends the results of classical parametric statistics like Fisher and Wilks theorem to modern setups with a high or infinite parameter dimension, limited sample size, and possible model misspecification. We consider a special…

We propose a new density estimation algorithm. Given $n$ i.i.d. observations from a distribution belonging to a class of densities on $\mathbb{R}^d$, our estimator outputs any density in the class whose "perceptron discrepancy" with the…

We consider a broad class of random bipartite networks, the distribution of which is invariant under permutation within each type of nodes. We are interested in $U$-statistics defined on the adjacency matrix of such a network, for which we…

The recent paper \cite{GSZ2023} on estimation and inference for top-ranking problem in Bradley-Terry-Lice (BTL) model presented a surprising result: component-wise estimation and inference can be done under much weaker conditions on the…

For nonparametric inference about a function, multiscale testing procedures resolve the need for bandwidth selection and achieve asymptotically optimal detection performance against a broad range of alternatives. However, critical values…

Motivated by applications in deep learning, where the global Lipschitz continuity condition is often not satisfied, we examine the problem of sampling from distributions with super-linearly growing log-gradients. We propose a novel tamed…

In recent years, a variety of novel measures of dependence have been introduced being capable of characterizing diverse types of directed dependence, hence diverse types of how a number of predictor variables $\mathbf{X} = (X_1, \dots,…

Accurately identifying the extremal dependence structure in multivariate heavy-tailed data is a fundamental yet challenging task, particularly in financial applications. Following a recently proposed bootstrap-based testing procedure, we…

In statistics and machine learning, when we train a fitted model on available data, we typically want to ensure that we are searching within a model class that contains at least one accurate model -- that is, we would like to ensure an…

The family of Mat\'ern kernels are often used in spatial statistics, function approximation and Gaussian process methods in machine learning. One reason for their popularity is the presence of a smoothness parameter that controls, for…

Datasets consisting of objects such as shapes, networks, images, or signals overlaid on such geometric objects permeate data science. Such datasets are often equipped with metrics that quantify the similarity or divergence between any pair…

The nonparametric maximum likelihood estimator (NPMLE) in monotone binary regression models is studied when the impact of the features on the labels is weak. Here, weakness is colloquially understood as "close to flatness" of the…

This paper studies the construction of adaptive confidence intervals under Huber's contamination model when the contamination proportion is unknown. For the robust confidence interval of a Gaussian mean, we show that the optimal length of…

Building on recent studies of large-dimensional kernel regression, particularly those involving inner product kernels on the sphere $\mathbb{S}^{d}$, we investigate the Pinsker bound for inner product kernel regression in such settings.…

We derive a Bernstein von-Mises theorem in the context of misspecified, non-i.i.d., hierarchical models parametrized by a finite-dimensional parameter of interest. We apply our results to hierarchical models containing non-linear operators,…

Modern network datasets are often composed of multiple layers, either as different views, time-varying observations, or independent sample units, resulting in collections of networks over the same set of vertices but with potentially…