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Quantile regression, the prediction of conditional quantiles, finds applications in various fields. Often, some or all of the variables are discrete. The authors propose two new quantile regression approaches to handle such mixed…
We study causal inference in a multi-environment setting, in which the functional relations for producing the variables from their direct causes remain the same across environments, while the distribution of exogenous noises may vary. We…
The paper studies the asymptotic behaviour of weighted functionals of long-range dependent data over increasing observation windows. Various important statistics, including sample means, high order moments, occupation measures can be given…
High-dimensional multivariate longitudinal data, which arise when many outcome variables are measured repeatedly over time, are becoming increasingly common in social, behavioral and health sciences. We propose a latent variable model for…
We study theoretical predictive performance of ridge and ridge-less least-squares regression when covariate vectors arise from evaluating $p$ random, means-square continuous functions over a latent metric space at $n$ random and unobserved…
This paper investigates some aspects of the variational behaviour of nonsmooth functions, with special emphasis on certain stability phenomena. Relationships linking such properties as sharp minimality, superstability, error bound and…
We compare possibilities of extension of bounded and unbounded Baire-one functions from subspaces of topological spaces.
We generalize McDiarmid's inequality for functions with bounded differences on a high probability set, using an extension argument. Those functions concentrate around their conditional expectations. We further extend the results to…
We consider random networks whose dynamics is described by a rate equation, with transition rates $w_{nm}$ that form a symmetric matrix. The long time evolution of the system is characterized by a diffusion coefficient $D$. In one dimension…
Many policies hinge on a continuous variable exceeding a threshold, prompting strategic behavior by agents to stay on the favorable side. This creates density discontinuities at cutoffs, evident in contexts like taxable income, corporate…
In functional data analysis, functional linear regression has attracted significant attention recently. Herein, we consider the case where both the response and covariates are functions. There are two available approaches for addressing…
Despite of various similar features, Functional Data Analysis and High-Dimensional Data Analysis are two major fields in Statistics that grew up recently almost independently one from each other. The aim of this paper is to propose a survey…
Let D be a bounded domain in the complex plane whose boundary consists of m pairwise disjoint simple closed curves where m is greater than one. Let A(bD) be the algebra of all continuous functions on bD which extend holomorphically through…
Domain generalization aims to develop models that are robust to distribution shifts. Existing methods focus on learning invariance across domains to enhance model robustness, and data augmentation has been widely used to learn invariant…
We consider a positive recurrent one-dimensional diffusion process with continuous coefficients and we establish stable central limit theorems for a certain type of additive functionals of this diffusion. In other words we find some…
We consider multivariate splines and show that they have a random feature expansion as infinitely wide neural networks with one-hidden layer and a homogeneous activation function which is the power of the rectified linear unit. We show that…
A one-parameter deformation of a periodic bar-and-joint framework is expansive when all distances between joints increase or stay the same. In dimension two, expansive behavior can be fully explained through our theory of periodic…
We derive an exact and efficient Bayesian regression algorithm for piecewise constant functions of unknown segment number, boundary location, and levels. It works for any noise and segment level prior, e.g. Cauchy which can handle outliers.…
We give a general strategy to construct superoscillating/growing functions using an orthogonal polynomial expansion of a bandlimited function. The degree of superoscillation/growth is controlled by an anomalous expectation value of a…
In this paper, we develop a quantile functional regression modeling framework that models the distribution of a set of common repeated observations from a subject through the quantile function, which is regressed on a set of covariates to…