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This paper studies multivariate nonparametric change point localization and inference problems. The data consists of a multivariate time series with potentially short range dependence. The distribution of this data is assumed to be…

Statistics Theory · Mathematics 2023-01-30 Carlos Misael Madrid Padilla , Haotian Xu , Daren Wang , Oscar Hernan Madrid Padilla , Yi Yu

In this work, we propose new objective functions to train deep neural network based density ratio estimators and apply it to a change point detection problem. Existing methods use linear combinations of kernels to approximate the density…

Machine Learning · Computer Science 2019-05-27 Haidar Khan , Lara Marcuse , Bülent Yener

We analyze the $\ell_1$ and $\ell_\infty$ convergence rates of k nearest neighbor density estimation method. Our analysis includes two different cases depending on whether the support set is bounded or not. In the first case, the…

Machine Learning · Statistics 2020-10-02 Puning Zhao , Lifeng Lai

A nonparametric procedure for robust regression estimation and for quantile regression is proposed which is completely data-driven and adapts locally to the regularity of the regression function. This is achieved by considering in each…

Statistics Theory · Mathematics 2009-04-06 Markus Reiss , Yves Rozenholc , Charles-Andre Cuenod

In this paper, we introduce a robust nonparametric density estimator combining the popular Kernel Density Estimation method and the Median-of-Means principle (MoM-KDE). This estimator is shown to achieve robustness to any kind of anomalous…

Statistics Theory · Mathematics 2020-07-01 Pierre Humbert , Batiste Le Bars , Ludovic Minvielle , Nicolas Vayatis

Consider a Gaussian nonparametric regression problem having both an unknown mean function and unknown variance function. This article presents a class of difference-based kernel estimators for the variance function. Optimal convergence…

Statistics Theory · Mathematics 2009-09-29 Lawrence D. Brown , M. Levine

In classical density (or density-functional) estimation, it is standard to assume that the underlying distribution has a density with respect to the Lebesgue measure. However, when the data distribution is a mixture of continuous and…

Methodology · Statistics 2025-08-05 Aytijhya Saha , Aaditya Ramdas

Estimating the ratio of two probability densities from finitely many samples, is a central task in machine learning and statistics. In this work, we show that a large class of kernel methods for density ratio estimation suffers from error…

Machine Learning · Computer Science 2024-06-04 Lukas Gruber , Markus Holzleitner , Johannes Lehner , Sepp Hochreiter , Werner Zellinger

Given a sample $\{X_i\}_{i=1}^n$ from $f_X$, we construct kernel density estimators for $f_Y$, the convolution of $f_X$ with a known error density $f_{\epsilon}$. This problem is known as density estimation with Berkson error and has…

Methodology · Statistics 2014-07-30 James P. Long , Noureddine El Karoui , John A. Rice

We propose two classes of nonparametric point estimators of $\theta=P(X<Y)$ in the case where $(X,Y)$ are paired, possibly dependent, absolutely continuous random variables. The proposed estimators are based on nonparametric estimators of…

Methodology · Statistics 2013-03-27 J. A. Montoya , F. J. Rubio

In a previous article, a least square regression estimation procedure was proposed: first, we condiser a family of functions and study the properties of an estimator in every unidimensionnal model defined by one of these functions; we then…

Statistics Theory · Mathematics 2007-06-13 Pierre Alquier

The problem we concentrate on is as follows: given (1) a convex compact set $X$ in ${\mathbb{R}}^n$, an affine mapping $x\mapsto A(x)$, a parametric family $\{p_{\mu}(\cdot)\}$ of probability densities and (2) $N$ i.i.d. observations of the…

Statistics Theory · Mathematics 2009-08-24 Anatoli B. Juditsky , Arkadi S. Nemirovski

We study minimax convergence rates of nonparametric density estimation under a large class of loss functions called "adversarial losses", which, besides classical $\mathcal{L}^p$ losses, includes maximum mean discrepancy (MMD), Wasserstein…

Statistics Theory · Mathematics 2018-10-30 Shashank Singh , Ananya Uppal , Boyue Li , Chun-Liang Li , Manzil Zaheer , Barnabás Póczos

In this paper, we consider nonparametric multidimensional finite mixture models and we are interested in the semiparametric estimation of the population weights. Here, the i.i.d. observations are assumed to have at least three components…

Statistics Theory · Mathematics 2017-12-14 Elisabeth Gassiat , Judith Rousseau , Elodie Vernet

Recent advances have demonstrated the possibility of solving the deconvolution problem without prior knowledge of the noise distribution. In this paper, we study the repeated measurements model, where information is derived from multiple…

Statistics Theory · Mathematics 2024-09-04 Jérémie Capitao-Miniconi , Elisabeth Gassiat , Luc Lehéricy

We examine rules for predicting whether a point in $\mathbb{R}$ generated from a 50-50 mixture of two different probability distributions came from one distribution or the other, given limited (or no) information on the two distributions,…

Statistics Theory · Mathematics 2024-04-09 Kevin Bleakley

Given a set of points $P\subset \mathbb{R}^{d}$ and a kernel $k$, the Kernel Density Estimate at a point $x\in\mathbb{R}^{d}$ is defined as $\mathrm{KDE}_{P}(x)=\frac{1}{|P|}\sum_{y\in P} k(x,y)$. We study the problem of designing a data…

Data Structures and Algorithms · Computer Science 2018-09-03 Moses Charikar , Paris Siminelakis

In this paper, we study the nonparametric estimation of the density $f_\Delta$ of an increment of a L\'evy process $X$ based on $n$ observations with a sampling rate $\Delta$. The class of L\'evy processes considered is broad, including…

Statistics Theory · Mathematics 2024-11-04 Céline Duval , Taher Jalal , Ester Mariucci

We study mixture of linear regression (random coefficient) models, which capture population heterogeneity by allowing the regression coefficients to follow an unknown distribution $G^*$. In contrast to common parametric methods that fix the…

Methodology · Statistics 2025-07-01 Hansheng Jiang , Adityanand Guntuboyina

A nonparametric kernel density estimator for directional-linear data is introduced. The proposal is based on a product kernel accounting for the different nature of both (directional and linear) components of the random vector. Expressions…