Related papers: Efficiency of Z-estimators indexed by the objectiv…

This paper addresses the problem of regression to reconstruct functions, which are observed with superimposed errors at random locations. We address the problem in reproducing kernel Hilbert spaces. It is demonstrated that the estimator,…

It is shown that the radial averaging operator $$ T_\omega(f)(z)=\frac{\int_{|z|}^1f\left(s\frac{z}{|z|}\right)\omega(s)\,ds}{\widehat{\omega}(z)},\quad \widehat{\omega}(z)=\int_{|z|}^1\omega(s)\,ds, $$ induced by a radial weight $\omega$…

The problem of simultaneous estimation of location/scale parameters $\theta_1$ and $\theta_2$ of a general bivariate location/scale model, when the ordering between the parameters is known apriori (say, $\theta_1\leq \theta_2$), has been…

Let $X$ be a real prehomogeneous vector space under a reductive group $G$, such that $X$ is an absolutely spherical $G$-variety with affine open orbit. We define local zeta integrals that involve the integration of Schwartz-Bruhat functions…

Functional autoregressive models of order one (FAR(1)) are predominantly estimated by projecting curves onto leading functional principal components and fitting a vector autoregression in score space, requiring a discrete truncation level…

It is a well-known fact that in a Lipschitz domain \Omega\subset R^n a p-Hardy inequality, with weight d(x,\partial\Omega)^\beta, holds for all u\in C_0^\infty(\Omega) whenever \beta<p-1. We show that actually the same is true under the…

For many applications, an ensemble of base classifiers is an effective solution. The tuning of its parameters(number of classes, amount of data on which each classifier is to be trained on, etc.) requires G, the generalization error of a…

Test-time alignment (TTA) aims to adapt models to specific rewards during inference. However, existing methods tend to either under-optimise or over-optimise (reward hack) the target reward function. We propose Null-Text Test-Time Alignment…

We review generalized zeta functions built over the Riemann zeros (in short: "superzeta" functions). They are symmetric functions of the zeros that display a wealth of explicit properties, fully matching the much more elementary Hurwitz…

This paper studies the identification and estimation of weighted average derivatives of conditional location functionals including conditional mean and conditional quantiles in settings where either the outcome variable or a regressor is…

The presence of distribution shifts poses a significant challenge for deploying modern machine learning models in real-world applications. This work focuses on the target shift problem in a regression setting (Zhang et al., 2013; Nguyen et…

We provide a unified approach to a method of estimation of the regression parameter in balanced linear models with a structured covariance matrix that combines a high breakdown point and bounded influence with high asymptotic efficiency at…

Let $\{P_{\theta}:\theta \in {\mathbb R}^d\}$ be a log-concave location family with $P_{\theta}(dx)=e^{-V(x-\theta)}dx,$ where $V:{\mathbb R}^d\mapsto {\mathbb R}$ is a known convex function and let $X_1,\dots, X_n$ be i.i.d. r.v. sampled…

We consider the problem of consistently estimating the conditional distribution $P(Y \in A |X)$ of a functional data object $Y=(Y(t): t\in[0,1])$ given covariates $X$ in a general space, assuming that $Y$ and $X$ are related by a functional…

We study weighted Sobolev inequalities on open convex cones endowed with $\alpha$-homogeneous weights satisfying a certain concavity condition. We establish a so-called reduction principle for these inequalities and characterize optimal…

We improve the universality theorem of the Riemann zeta-function in short intervals by establishing universality for significantly shorter intervals $[T,T+H]$. Assuming the Riemann Hypothesis, we prove that universality in such short…

This paper investigates test-time adaptation (TTA) for regression, where a regression model pre-trained in a source domain is adapted to an unknown target distribution with unlabeled target data. Although regression is one of the…

In this note, we investigate the renorming theory of Banach spaces with property $(\beta)$ of Rolewicz. In particular, we give a "coordinate-free" proof of the fact that every Banach space with property $(\beta)$ admits an equivalent norm…

There is growing interest in developing statistical estimators that achieve exponential concentration around a population target even when the data distribution has heavier than exponential tails. More recent activity has focused on…

Greedy algorithms which use only function evaluations are applied to convex optimization in a general Banach space $X$. Along with algorithms that use exact evaluations, algorithms with approximate evaluations are treated. A priori upper…