Related papers: Universal kernel-type estimation of random fields
Convergence rates of kernel density estimators for stationary time series are well studied. For invertible linear processes, we construct a new density estimator that converges, in the supremum norm, at the better, parametric, rate…
Kernel methods, particularly kernel ridge regression (KRR), are time-proven, powerful nonparametric regression techniques known for their rich capacity, analytical simplicity, and computational tractability. The analysis of their predictive…
Penalties that induce smoothness are common in nonparametric regression. In many settings, the amount of smoothness in the data generating function will not be known. Simon and Shojaie (2021) derived convergence rates for nonparametric…
The problem of establishing out-of-sample bounds for the values of an unkonwn ground-truth function is considered. Kernels and their associated Hilbert spaces are the main formalism employed herein along with an observational model where…
This study proposes a debiasing method for smooth nonparametric estimators. While machine learning techniques such as random forests and neural networks have demonstrated strong predictive performance, their theoretical properties remain…
Let $i=1,\ldots,N$ index a simple random sample of units drawn from some large population. For each unit we observe the vector of regressors $X_{i}$ and, for each of the $N\left(N-1\right)$ ordered pairs of units, an outcome $Y_{ij}$. The…
The celebrated Nadaraya-Watson kernel estimator is among the most studied method for nonparametric regression. A classical result is that its rate of convergence depends on the number of covariates and deteriorates quickly as the dimension…
This paper deals with the nonparametric density estimation of the regression error term assuming its independence with the covariate. The difference between the feasible estimator which uses the estimated residuals and the unfeasible one…
This paper studies the non-parametric estimation and uniform inference for the conditional quantile regression function (CQRF) with covariates exposed to measurement errors. We consider the case that the distribution of the measurement…
We introduce a nonparametric way to estimate the global probability density function for a random persistence diagram. Precisely, a kernel density function centered at a given persistence diagram and a given bandwidth is constructed. Our…
One central theme in machine learning is function estimation from sparse and noisy data. An example is supervised learning where the elements of the training set are couples, each containing an input location and an output response. In the…
We provide uniform confidence bands for kernel ridge regression (KRR), a widely used nonparametric regression estimator for nonstandard data such as preferences, sequences, and graphs. Despite the prevalence of these data--e.g., student…
In this article, we introduce a kernel-based consensual aggregation method for regression problems. We aim to exibly combine individual regression estimators $r_1, \ldots, r_M$ using a weighted average where the weights are dened based on…
No matter the nature of the response and/or explanatory variables in a regression model, some basic issues such as the existence of an effect of the predictor on the response, or the assessment of a common shape across groups of…
Kernel ridge regression (KRR), also known as the least-squares support vector machine, is a fundamental method for learning functions from finite samples. While most existing analyses focus on the noisy setting with constant-level label…
The Nadaraya-Watson kernel estimator is among the most popular nonparameteric regression technique thanks to its simplicity. Its asymptotic bias has been studied by Rosenblatt in 1969 and has been reported in a number of related literature.…
We propose a new estimator for nonparametric binary choice models that does not impose a parametric structure on either the systematic function of covariates or the distribution of the error term. A key advantage of our approach is its…
In regression problems where covariates are naturally organized in a hierarchical tree structure, a central challenge is to select the resolution at which covariates enter the model. Determining this level of feature aggregation is of…
We investigate the issue of bandwidth estimation in a nonparametric functional regression model with function-valued, continuous real-valued and discrete-valued regressors under the framework of unknown error density. Extending from the…
Random Fourier Features (RFF) demonstrate wellappreciated performance in kernel approximation for largescale situations but restrict kernels to be stationary and positive definite. And for non-stationary kernels, the corresponding RFF could…