Related papers: Uniform in bandwidth exact rates for a class of ke…

Most machine learning methods require tuning of hyper-parameters. For kernel ridge regression with the Gaussian kernel, the hyper-parameter is the bandwidth. The bandwidth specifies the length scale of the kernel and has to be carefully…

Let $I=(a,b)\times(c,d)\subset {\mathbb R}_{+}^2$ be an index set and let $\{G_{\alpha}(x) \}_{\alpha \in I}$ be a collection of Gaussian functions, i.e. $G_{\alpha}(x) = \exp(-\alpha_1 x_1^2 - \alpha_2 x_2^2)$, where $\alpha = (\alpha_1,…

In this paper, we study the behavior of a kernel estimator of the regression function in the right censored model with $\alpha$-mixing data . The uniform strong consistency over a real compact set of the estimate is established along with a…

Kernel-based nonparametric hazard rate estimation is considered with a special class of infinite-order kernels that achieves favorable bias and mean square error properties. A fully automatic and adaptive implementation of a density and…

Conformal prediction, and split conformal prediction as a specific implementation, offer a distribution-free approach to estimating prediction intervals with statistical guarantees. Recent work has shown that split conformal prediction can…

Given additional distributional information in the form of moment restrictions, kernel density and distribution function estimators with implied generalised empirical likelihood probabilities as weights achieve a reduction in variance due…

We consider estimation and inference on average treatment effects under unconfoundedness conditional on the realizations of the treatment variable and covariates. Given nonparametric smoothness and/or shape restrictions on the conditional…

This paper considers the generation of prediction intervals (PIs) by neural networks for quantifying uncertainty in regression tasks. It is axiomatic that high-quality PIs should be as narrow as possible, whilst capturing a specified…

Kernel-based estimators such as local polynomial estimators in regression discontinuity designs are often evaluated at multiple bandwidths as a form of sensitivity analysis. However, if in the reported results, a researcher selects the…

In this paper we develop procedures to construct simultaneous confidence bands for $\tilde p$ potentially infinite-dimensional parameters after model selection for general moment condition models where $\tilde p$ is potentially much larger…

The angular measure on the unit sphere characterizes the first-order dependence structure of the components of a random vector in extreme regions and is defined in terms of standardized margins. Its statistical recovery is an important step…

Motivated by the need to analyze continuously updated data sets in the context of time-to-event modeling, we propose a novel nonparametric approach to estimate the conditional hazard function given a set of continuous and discrete…

Given random samples drawn i.i.d. from a probability measure $\mathbb{P}$ (defined on say, $\mathbb{R}^d$), it is well-known that the empirical estimator is an optimal estimator of $\mathbb{P}$ in weak topology but not even a consistent…

Generative models are often conditioned on a small set of examples via cross-attention. Under the Gaussian optimal-transport path, we show that the exact velocity field induced by a finite support set is a Nadaraya--Watson kernel smoother…

Conformal prediction provides distribution-free prediction sets with finite-sample conditional guarantees. We build upon the RKHS-based framework of Gibbs et al. (2023), which leverages families of covariate shifts to provide approximate…

We provide improved error bounds for kernel-based numerical differentiation in terms of growth functions when kernels are of a finite smoothness, such as polyharmonic splines, thin plate splines or Wendland kernels. In contrast to existing…

Modern construction of uniform confidence bands for nonparametric densities (and other functions) often relies on the classical Smirnov-Bickel-Rosenblatt (SBR) condition; see, for example, Gin\'{e} and Nickl [Probab. Theory Related Fields…

We show that if $\mathcal{X}$ is a complete separable metric space and $\mathcal{C}$ is a countable family of Borel subsets of $\mathcal{X}$ with finite VC dimension, then, for every stationary ergodic process with values in $\mathcal{X}$,…

Previous influential work showed that infinite width limits of neural networks in the lazy training regime are described by kernel machines. Here, we show that neural networks trained in the rich, feature learning infinite-width regime in…

Generalizing the bounded kernel results of Borgs, Chayes, Lov\'asz, S\'os and Vesztergombi (2008), we prove two Sampling Lemmas for unbounded kernels with respect to the cut norm. On the one hand, we show that given a (symmetric) kernel…