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Nonparametric kernel density estimation is a very natural procedure which simply makes use of the smoothing power of the convolution operation. Yet, it performs poorly when the density of a positive variable is to be estimated (boundary…

Statistics Theory · Mathematics 2017-07-17 Gery Geenens

The present paper studies density deconvolution in the presence of small Berkson errors, in particular, when the variances of the errors tend to zero as the sample size grows. It is known that when the Berkson errors are present, in some…

Statistics Theory · Mathematics 2018-10-17 Ramchandra Rimal , Marianna Pensky

We provide new asymptotic theory for kernel density estimators, when these are applied to autoregressive processes exhibiting moderate deviations from a unit root. This fills a gap in the existing literature, which has to date considered…

Statistics Theory · Mathematics 2019-08-19 James A. Duffy

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

Unlinked regression, in which covariates and responses are observed separately without known correspondence, has recently gained increasing attention. Deconvolution, on the other hand, is a fundamental and challenging problem in…

Statistics Theory · Mathematics 2026-05-19 Fadoua Balabdaoui , Antonio Di Noia , Cécile Durot

Stochastic volatility modelling of financial processes has become increasingly popular. The proposed models usually contain a stationary volatility process. We will motivate and review several nonparametric methods for estimation of the…

Methodology · Statistics 2014-07-15 Bert van Es , Peter Spreij , Harry van Zanten

Kernel density estimation is a popular method for estimating unseen probability distributions. However, the convergence of these classical estimators to the true density slows down in high dimensions. Moreover, they do not define meaningful…

Statistics Theory · Mathematics 2025-05-30 Jack Kendrick

We derive asymptotic normality of kernel type deconvolution estimators of the density, the distribution function at a fixed point, and of the probability of an interval. We consider the so called super smooth case where the characteristic…

Statistics Theory · Mathematics 2007-06-13 A. J. van Es , H. -W. Uh

In numerous applications data are observed at random times and an estimated graph of the spectral density may be relevant for characterizing and explaining phenomena. By using a wavelet analysis, one derives a nonparametric estimator of the…

Statistics Theory · Mathematics 2009-11-27 Jean-Marc Bardet , Pierre Bertrand

We consider nonparametric regression with functional covariates, that is, they are elements of an infinite-dimensional Hilbert space. A locally polynomial estimator is constructed, where an orthonormal basis and various tuning parameters…

Statistics Theory · Mathematics 2025-04-09 Moritz Jirak , Alois Kneip , Alexander Meister , Mario Pahl

In this paper we develop a nonparametric regression method that is simultaneously adaptive over a wide range of function classes for the regression function and robust over a large collection of error distributions, including those that are…

Statistics Theory · Mathematics 2008-10-28 Lawrence D. Brown , T. Tony Cai , Harrison H. Zhou

It is a typical standard assumption in the density deconvolution problem that the characteristic function of the measurement error distribution is non-zero on the real line. While this condition is assumed in the majority of existing works…

Statistics Theory · Mathematics 2021-01-08 Alexander Goldenshluger , Taeho Kim

We consider the model $Z_i=X_i+\varepsilon_i$, for i.i.d. $X_i$'s and $\varepsilon_i$'s and independent sequences $(X_i)_{i\in{\mathbb{N}}}$ and $(\varepsilon_i)_{i\in{\mathbb{N}}}$. The density $f_{\varepsilon}$ of $\varepsilon_1$ is…

Statistics Theory · Mathematics 2009-02-10 C. Butucea , F. Comte

In this paper we study the problem of density deconvolution under general assumptions on the measurement error distribution. Typically deconvolution estimators are constructed using Fourier transform techniques, and it is assumed that the…

Statistics Theory · Mathematics 2020-02-04 Denis Belomestny , Alexander Goldenshluger

The paper considers nonparametric kernel density/regression estimation from a stochastic optimization point of view. The estimation problem is represented through a family of stochastic optimization problems. Recursive constrained…

Statistics Theory · Mathematics 2024-09-05 Vladimir Norkin , Vladimir Kirilyuk

We study the posterior contraction rates of a Bayesian method with Gaussian process priors in nonparametric regression and its plug-in property for differential operators. For a general class of kernels, we establish convergence rates of…

Statistics Theory · Mathematics 2020-12-01 Zejian Liu , Meng Li

For highly skewed or fat-tailed distributions, mean or median-based methods often fail to capture the central tendencies in the data. Despite being a viable alternative, estimating the conditional mode given certain covariates (or mode…

Econometrics · Economics 2024-12-10 Eduardo Schirmer Finn , Eduardo Horta

We consider a recurrent Markov process which is an It\^o semi-martingale. The L\'evy kernel describes the law of its jumps. Based on observations X(0),X({\Delta}),...,X(n{\Delta}), we construct an estimator for the L\'evy kernel's density.…

Statistics Theory · Mathematics 2013-05-14 Florian A. J. Ueltzhöfer

In the context of regressing a response $Y$ on a predictor $X$, we consider estimating the local modes of the distribution of $Y$ given $X=x$ when $X$ is prone to measurement error. We propose two nonparametric estimation methods, with one…

Methodology · Statistics 2016-10-28 Haiming Zhou , Xianzheng Huang

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…

Statistics Theory · Mathematics 2013-08-07 Aboubacar Amiri , Christophe Crambes , Baba Thiam