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We consider the estimation of two-sample integral functionals, of the type that occur naturally, for example, when the object of interest is a divergence between unknown probability densities. Our first main result is that, in wide…

Statistics Theory · Mathematics 2023-01-31 Thomas B. Berrett , Richard J. Samworth

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

We study theoretically, for the first time, the Dirichlet kernel estimator introduced by Aitchison and Lauder (1985) for the estimation of multivariate densities supported on the $d$-dimensional simplex. The simplex is an important case as…

Statistics Theory · Mathematics 2021-10-12 Frédéric Ouimet , Raimon Tolosana-Delgado

Unbiased and consistent variance estimators generally do not exist for design-based treatment effect estimators because experimenters never observe more than one potential outcome for any unit. The problem is exacerbated by interference and…

Methodology · Statistics 2024-07-04 Christopher Harshaw , Joel A. Middleton , Fredrik Sävje

For the zone of moderate deviation probabilities the local asymptotic minimax lower bound of asymptotic efficiency of estimators is established. The estimation parameter is multidimensional. The lower bound admits the interpretation as the…

Statistics Theory · Mathematics 2012-06-08 Mikhail Ermakov

A mean function in reproducing kernel Hilbert space, or a kernel mean, is an important part of many applications ranging from kernel principal component analysis to Hilbert-space embedding of distributions. Given finite samples, an…

Machine Learning · Statistics 2013-06-07 Krikamol Muandet , Kenji Fukumizu , Bharath Sriperumbudur , Arthur Gretton , Bernhard Schölkopf

The main purpose of this paper is to introduce and study the behavior of minimum {\phi}-divergence estimators as an alternative to the maximum likelihood estimator in latent class models for binary items. As it will become clear below,…

Methodology · Statistics 2014-06-03 Ángel Felipe , Pedro Miranda , Leandro Pardo

Biased stochastic estimators, such as finite-differences for noisy gradient estimation, often contain parameters that need to be properly chosen to balance impacts from the bias and the variance. While the optimal order of these parameters…

Methodology · Statistics 2019-02-14 Henry Lam , Xinyu Zhang , Xuhui Zhang

This article investigates nonparametric estimation of variance functions for functional data when the mean function is unknown. We obtain asymptotic results for the kernel estimator based on squared residuals. Similar to the finite…

Methodology · Statistics 2008-12-16 Heng Lian

Bernstein estimators are well-known to avoid the boundary bias problem of traditional kernel estimators. The theoretical properties of these estimators have been studied extensively on compact intervals and hypercubes, but never on the…

Statistics Theory · Mathematics 2022-05-25 Frédéric Ouimet

We herein establish an asymptotic representation theorem for locally asymptotically normal quantum statistical models. This theorem enables us to study the asymptotic efficiency of quantum estimators such as quantum regular estimators and…

Quantum Physics · Physics 2024-11-14 Akio Fujiwara , Koichi Yamagata

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

In this paper a new family of minimum divergence estimators based on the Bregman divergence is proposed, where the defining convex function has an exponential nature. These estimators avoid the necessity of using an intermediate kernel…

Methodology · Statistics 2019-11-25 Taranga Mukherjee , Abhijit Mandal , Ayanendranath Basu

This paper considers extensions of minimum-disparity estimators to the problem of estimating parameters in a regression model that is conditionally specified; that is where a parametric model describes the distribution of a response $y$…

Statistics Theory · Mathematics 2016-02-10 Giles Hooker

Multivariate kernel density estimations have received much spate of interest. In addition to conventional methods of (non-)classical associated-kernels for (un)bounded densities and bandwidth selections, the multiple extended-beta kernel…

Statistics Theory · Mathematics 2025-02-11 Sobom M. Somé , Célestin C. Kokonendji , Francial G. B. Libengué Dobélé-Kpoka

In frequentist inference, minimizing the Hellinger distance between a kernel density estimate and a parametric family produces estimators that are both robust to outliers and statistically efficienty when the parametric model is correct.…

Statistics Theory · Mathematics 2018-12-12 Yuefeng Wu , Giles Hooker

Coresets have emerged as a powerful tool to summarize data by selecting a small subset of the original observations while retaining most of its information. This approach has led to significant computational speedups but the performance of…

Statistics Theory · Mathematics 2020-12-10 Paxton Turner , Jingbo Liu , Philippe Rigollet

We propose an estimator of the kernel-based conditional mean dependence measure obtained from an appropriate modification of a naive estimator based on usual empirical estimators. We then get asymptotic normality of this estimator both…

Statistics Theory · Mathematics 2022-07-27 Terence Kevin Manfoumbi Djonguet , Guy Martial Nkiet

This paper examines asymptotic properties of local M-estimators under three sets of high-level conditions. These conditions are sufficiently general to cover the minimum volume predictive region, conditional maximum score estimator for a…

Statistics Theory · Mathematics 2020-01-15 Myung Hwan Seo , Taisuke Otsu

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