Related papers: Effects of associated kernels in nonparametric mul…

I propose kernel ridge regression estimators for nonparametric dose response curves and semiparametric treatment effects in the setting where an analyst has access to a selected sample rather than a random sample; only for select…

The main purpose is to estimate the regression function of a real random variable with functional explanatory variable by using a recursive nonparametric kernel approach. The mean square error and the almost sure convergence of a family of…

We introduce a general method to prove uniform in bandwidth consistency of kernel-type function estimators. Examples include the kernel density estimator, the Nadaraya-Watson regression estimator and the conditional empirical process. Our…

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…

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…

Modern Bayesian optimization and adaptive sampling methods increasingly rely on nonlinear parametric models, yet theoretical guarantees for such models under adaptive data collection remain limited. Existing analyses largely focus on…

As with classic statistics, functional regression models are invaluable in the analysis of functional data. While there are now extensive tools with accompanying theory available for linear models, there is still a great deal of work to be…

In a regression model, we write the Nadaraya-Watson estimator of the regression function as the quotient of two kernel estimators, and propose a bandwidth selection method for both the numerator and the denominator. We prove risk bounds for…

This paper introduces the kernel mixture network, a new method for nonparametric estimation of conditional probability densities using neural networks. We model arbitrarily complex conditional densities as linear combinations of a family of…

In biomedical studies, we are often interested in the association between different types of covariates and the times to disease events. Because the relationship between the covariates and event times is often complex, standard survival…

We apply local laws of random matrices and free probability theory to study the spectral properties of two kernel-based sensor fusion algorithms, nonparametric canonical correlation analysis (NCCA) and alternating diffusion (AD), for two…

Continuous treatments (e.g., doses) arise often in practice, but many available causal effect estimators are limited by either requiring parametric models for the effect curve, or by not allowing doubly robust covariate adjustment. We…

We consider the kernel partial least squares algorithm for non-parametric regression with stationary dependent data. Probabilistic convergence rates of the kernel partial least squares estimator to the true regression function are…

Compared to nonparametric estimators in the multivariate setting, kernel estimators for functional data models have a larger order of bias. This is problematic for constructing confidence regions or statistical tests since the bias might…

In this paper we propose a variable bandwidth kernel regression estimator for $i.i.d.$ observations in $\mathbb{R}^2$ to improve the classical Nadaraya-Watson estimator. The bias is improved to the order of $O(h_n^4)$ under the condition…

In supervised learning, the output variable to be predicted is often represented as a function, such as a spectrum or probability distribution. Despite its importance, functional output regression remains relatively unexplored. In this…

This paper provides the theory about the convergence rate of the tilted version of linear smoother. We study tilted linear smoother, a nonparametric regression function estimator, which is obtained by minimizing the distance to an infinite…

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 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.…

This paper proposes nonparametric kernel-smoothing estimation for panel data to examine the degree of heterogeneity across cross-sectional units. We first estimate the sample mean, autocovariances, and autocorrelations for each unit and…