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There has been substantial recent work on methods for estimating the slope function in linear regression for functional data analysis. However, as in the case of more conventional finite-dimensional regression, much of the practical…

Statistics Theory · Mathematics 2007-06-13 T. Tony Cai , Peter Hall

The paper considers functional linear regression, where scalar responses $Y_1,...,Y_n$ are modeled in dependence of random functions $X_1,...,X_n$. We propose a smoothing splines estimator for the functional slope parameter based on a…

Statistics Theory · Mathematics 2009-02-26 Christophe Crambes , Alois Kneip , Pascal Sarda

For nonparametric regression with one-sided errors and a boundary curve model for Poisson point processes we consider the problem of efficient estimation for linear functionals. The minimax optimal rate is obtained by an unbiased estimation…

Statistics Theory · Mathematics 2015-09-25 Markus Reiß , Leonie Selk

When using the bootstrap in the presence of measurement error, we must first estimate the target distribution function; we cannot directly resample, since we do not have a sample from the target. These and other considerations motivate the…

Statistics Theory · Mathematics 2008-10-28 Peter Hall , Soumendra N. Lahiri

For a multidimensional It\^o semimartingale, we consider the problem of estimating integrated volatility functionals. Jacod and Rosenbaum (2013) studied a plug-in type of estimator based on a Riemann sum approximation of the integrated…

Econometrics · Economics 2025-09-09 José E. Figueroa-López , Jincheng Pang , Bei Wu

This paper investigates the state estimation problem for a class of complex networks, in which the dynamics of each node is subject to Gaussian noise, system uncertainties and nonlinearities. Based on a regularized least-squares approach,…

Systems and Control · Electrical Eng. & Systems 2021-03-16 Peihu Duan , Qishao Wang , Zhisheng Duan , Guanrong Chen

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

The main result of this paper is a general central limit theorem for distributions defined by certain renewal type equations. We apply this to weakly self-avoiding random walks. We give good error estimates and Gaussian tail estimates which…

Probability · Mathematics 2007-05-23 Erwin Bolthausen , Christine Ritzmann

We consider a high-dimensional linear regression problem. Unlike many papers on the topic, we do not require sparsity of the regression coefficients; instead, our main structural assumption is a decay of eigenvalues of the covariance matrix…

Statistics Theory · Mathematics 2021-10-01 Igor Silin , Jianqing Fan

Kernel methods for deconvolution have attractive features, and prevail in the literature. However, they have disadvantages, which include the fact that they are usually suitable only for cases where the error distribution is infinitely…

Statistics Theory · Mathematics 2009-09-29 Peter Hall , Alexander Meister

In this paper we prove a uniform Fourier restriction estimate over the class of simple curves where the last coordinate function can be extended to a holomorphic function of bounded frequency in a sufficiently large disc. The proof is based…

Classical Analysis and ODEs · Mathematics 2023-03-31 Jaume de Dios Pont , Helge Jørgen Samuelsen

Central limit theorems play an important role in the study of statistical inference for stochastic processes. However, when the nonparametric local polynomial threshold estimator, especially local linear case, is employed to estimate the…

Probability · Mathematics 2017-02-06 Yuping Song , Hanchao Wang

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…

Methodology · Statistics 2019-10-08 Vitaliy Oryshchenko , Richard J. Smith

In this paper, a class of statistics based on high frequency observations of oscillating and skew Brownian motion is considered. Their convergence rate towards the local time of the underlying process is obtained in form of a functional…

Probability · Mathematics 2024-04-04 Sara Mazzonetto

The Central Limit Theorem (CLT) establishes that sufficiently large sequences of independent and identically distributed random variables converge in probability to a normal distribution. This makes the CLT a fundamental building block of…

Logic in Computer Science · Computer Science 2026-03-10 Henning Basold , Oisín Flynn-Connolly , Chase Ford , Hao Wang

In this paper, we introduce a fundamental model for independent and identically distributed sequence with model uncertainty on the canonical space $(\mathbb{R}^\mathbb{N},\mathcal{B}(\mathbb{R}^\mathbb{N}))$ via probability kernels. Thanks…

Probability · Mathematics 2023-07-25 Xiaofan Guo , Xinpeng Li

We consider Betti numbers of the excursion of a smooth Euclidean Gaussian field restricted to a rectangular window, in the asymptotics where the window grows to R^d . With motivations coming from Topological Data Analysis, we derive a…

Probability · Mathematics 2025-12-16 Christian Hirsch , Raphaël Lachièze-Rey

This paper provides new uniform rate results for kernel estimators of absolutely regular stationary processes that are uniform in the bandwidth and in infinite-dimensional classes of dependent variables and regressors. Our results are…

Econometrics · Economics 2020-05-21 Juan Carlos Escanciano

A reduced-bias nonparametric estimator of the cumulative distribution function (CDF) and the survival function is proposed using infinite-order kernels. Fourier transform theory on generalized functions is utilized to obtain the improved…

Methodology · Statistics 2009-03-18 Arthur Berg , Dimitris N. Politis

Deconvolution is a statistical inverse problem to estimate the distribution of a random variable based on its noisy observations. Despite the extensive studies on the topic, deconvolution with unknown noise distribution remains as a…

Statistics Theory · Mathematics 2020-04-06 Devavrat Shah , Dogyoon Song