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We provide a theoretical foundation for non-parametric estimation of functions of random variables using kernel mean embeddings. We show that for any continuous function $f$, consistent estimators of the mean embedding of a random variable…

Machine Learning · Statistics 2018-06-04 Carl-Johann Simon-Gabriel , Adam Ścibior , Ilya Tolstikhin , Bernhard Schölkopf

New local linear estimators are proposed for a wide class of nonparametric regression models. The estimators are uniformly consistent regardless of satisfying traditional conditions of depen\-dence of design elements. The estimators are the…

Statistics Theory · Mathematics 2022-07-05 Yuliana Linke , Igor Borisov , Pavel Ruzankin , Vladimir Kutsenko , Elena Yarovaya , Svetlana Shalnova

We consider nonparametric estimation of the derivative of a probability density function with the bounded support on $[0,\infty)$. Estimates are looked up in the class of estimates with asymmetric gamma kernel functions. The use of gamma…

Probability · Mathematics 2014-07-10 A. V. Dobrovidov , L. A Markovich

We study optimal procedures for estimating a linear functional based on observational data. In many problems of this kind, a widely used assumption is strict overlap, i.e., uniform boundedness of the importance ratio, which measures how…

Statistics Theory · Mathematics 2023-01-18 Wenlong Mou , Peng Ding , Martin J. Wainwright , Peter L. Bartlett

The paper deals with the nonparametric estimation problem at a given fixed point for an autoregressive model with unknown distributed noise. Kernel estimate modifications are proposed. Asymptotic minimax and efficiency properties for…

Statistics Theory · Mathematics 2008-06-19 Ouerdia Arkoun , Serguei Pergamenchtchikov

In this paper, we establish minimax optimal rates of convergence for prediction in a semi-functional linear model that consists of a functional component and a less smooth nonparametric component. Our results reveal that the smoother…

Statistics Theory · Mathematics 2021-11-01 Keli Guo , Jun Fan , Lixing Zhu

Multivariate associated kernel estimators, which depend on both target point and bandwidth matrix, are appropriate for partially or totally bounded distributions and generalize the classical ones as Gaussian. Previous studies on…

Statistics Theory · Mathematics 2021-09-08 Célestin C. Kokonendji , Sobom M. Somé

Kernel quadrature is widely used to approximate integrals of smooth functions, with worst-case error typically decaying at the minimax rate $n^{-\alpha/d}$ for smoothness $\alpha$ in dimension $d$. Existing rate-optimal methods often depend…

Computation · Statistics 2026-05-19 Edoardo Bandoni , Christian Robert , Julien Stoehr

Extending the ideas of [7], this paper aims at providing a kernel based non-parametric estimation of a new class of time varying AR(1) processes (Xt), with local stationarity and periodic features (with a known period T), inducing the…

Statistics Theory · Mathematics 2018-11-13 Jean-Marc Bardet , Paul Doukhan

A method for estimating the conditional average treatment effect under condition of censored time-to-event data called BENK (the Beran Estimator with Neural Kernels) is proposed. The main idea behind the method is to apply the Beran…

Machine Learning · Computer Science 2022-11-22 Stanislav R. Kirpichenko , Lev V. Utkin , Andrei V. Konstantinov

Estimating the kernel mean in a reproducing kernel Hilbert space is a critical component in many kernel learning algorithms. Given a finite sample, the standard estimate of the target kernel mean is the empirical average. Previous works…

Machine Learning · Computer Science 2021-07-13 Xiaobo Xia , Shuo Shan , Mingming Gong , Nannan Wang , Fei Gao , Haikun Wei , Tongliang Liu

Averaging provides an alternative to bandwidth selection for density kernel estimation. We propose a procedure to combine linearly several kernel estimators of a density obtained from different, possibly data-driven, bandwidths. The method…

Statistics Theory · Mathematics 2019-11-05 O. Chernova , F. Lavancier , P. Rochet

We study the problem of the nonparametric estimation for the density $\pi$ of the stationary distribution of a $d$-dimensional stochastic differential equation $(X_t)_{t \in [0, T]}$. From the continuous observation of the sampling path on…

Statistics Theory · Mathematics 2023-10-23 Chiara Amorino , Arnaud Gloter

In this review we cover the basics of efficient nonparametric parameter estimation (also called functional estimation), with a focus on parameters that arise in causal inference problems. We review both efficiency bounds (i.e., what is the…

Methodology · Statistics 2023-01-27 Edward H. Kennedy

Estimating the innovation probability density is an important issue in any regression analysis. This paper focuses on functional autoregressive models. A residual-based kernel estimator is proposed for the innovation density. Asymptotic…

Methodology · Statistics 2010-05-07 Nadine Hilgert , Bruno Portier

We prove conditional asymptotic normality of a class of quadratic U-statistics that are dominated by their degenerate second order part and have kernels that change with the number of observations. These statistics arise in the construction…

Methodology · Statistics 2015-12-09 James Robins , Lingling Li , Eric Tchetgen Tchetgen , Aad van der Vaart

Combining information both within and between sample realizations, we propose a simple estimator for the local regularity of surfaces in the functional data framework. The independently generated surfaces are measured with errors at…

Statistics Theory · Mathematics 2023-10-03 Omar Kassi , Nicolas Klutchnikoff , Valentin Patilea

We prove absolute regularity ($\beta$-mixing) for nonstationary and multivariate versions of two popular classes of integer-valued processes. We show how this result can be used to prove asymptotic normality of a least squares estimator of…

Statistics Theory · Mathematics 2024-08-29 Zinsou Max Debaly , Michael H. Neumann , Lionel Truquet

Kernel smoothers are considered near the boundary of the interval. Kernels which minimize the expected mean square error are derived. These kernels are equivalent to using a linear weighting function in the local polynomial regression. It…

Methodology · Statistics 2019-12-03 Alexander Sidorenko , Kurt S. Riedel

This paper investigates asymptotic properties of algorithms that can be viewed as robust analogues of the classical empirical risk minimization. These strategies are based on replacing the usual empirical average by a robust proxy of the…

Statistics Theory · Mathematics 2023-06-01 Stanislav Minsker