Related papers: Kernel-Based Nonparametric Tests For Shape Constra…
Regularized empirical risk minimization including support vector machines plays an important role in machine learning theory. In this paper regularized pairwise learning (RPL) methods based on kernels will be investigated. One example is…
In nonparametric regression analysis, errors are possibly correlated in practice, and neglecting error correlation can undermine most bandwidth selection methods. When no prior knowledge or parametric form of the correlation structure is…
We study kernel-based estimation of nonparametric time-varying parameters (TVPs) in linear models. Our contributions are threefold. First, we establish consistency and asymptotic normality of the kernel-based estimator for a broad class of…
Needlets have been recognized as state-of-the-art tools to tackle spherical data, due to their excellent localization properties in both spacial and frequency domains. This paper considers developing kernel methods associated with the…
We present a general variational framework for the training of freeform nonlinearities in layered computational architectures subject to some slope constraints. The regularization that we add to the traditional training loss penalizes the…
Elliptical distribution is a basic assumption underlying many multivariate statistical methods. For example, in sufficient dimension reduction and statistical graphical models, this assumption is routinely imposed to simplify the data…
A kernelization is an efficient algorithm that given an instance of a parameterized problem returns an equivalent instance of size bounded by some function of the input parameter value. It is quite well understood which problems do or…
We study prediction-powered conditional inference in the setting where labeled data are scarce, unlabeled covariates are abundant, and a black-box machine-learning predictor is available. The goal is to perform statistical inference on…
We investigate the nonparametric estimation for regression in a fixed-design setting when the errors are given by a field of dependent random variables. Sufficient conditions for kernel estimators to converge uniformly are obtained. These…
This paper develops tests for inequality constraints of nonparametric regression functions. The test statistics involve a one-sided version of $L_p$-type functionals of kernel estimators $(1 \leq p < \infty)$. Drawing on the approach of…
We consider testing the significance of a subset of covariates in a nonparametric regression. These covariates can be continuous and/or discrete. We propose a new kernel-based test that smoothes only over the covariates appearing under the…
We consider parametrized problems driven by spatially nonlocal integral operators with parameter-dependent kernels. In particular, kernels with varying nonlocal interaction radius $\delta > 0$ and fractional Laplace kernels, parametrized by…
Variational methods are widely used for approximate posterior inference. However, their use is typically limited to families of distributions that enjoy particular conjugacy properties. To circumvent this limitation, we propose a family of…
We develop a unified theory of designs for controlled experiments that balance baseline covariates a priori (before treatment and before randomization) using the framework of minimax variance and a new method called kernel allocation. We…
In this work, we extend the classical framework of quantization for Borel probability measures defined on normed spaces $\mathbb{R}^k$ by introducing and analyzing the notions of the $n$th constrained quantization error, constrained…
The mainstream theory of hypothesis testing in high-dimensional regression typically assumes the underlying true model is a low-dimensional linear regression model, yet the Box-Cox transformation is a regression technique commonly used to…
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…
Financial econometrics has become an increasingly popular research field. In this paper we review a few parametric and nonparametric models and methods used in this area. After introducing several widely used continuous-time and…
Kernelization investigates exact preprocessing algorithms with performance guarantees. The most prevalent type of parameters used in kernelization is the solution size for optimization problems; however, also structural parameters have been…
In this paper, we are concerned with the generalization performance of non-parametric estimation for pairwise learning. Most of the existing work requires the hypothesis space to be convex or a VC-class, and the loss to be convex. However,…