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In this paper, we consider an unknown functional estimation problem in a general nonparametric regression model with the feature of having both multiplicative and additive noise.We propose two new wavelet estimators in this general context.…

Statistics Theory · Mathematics 2020-12-25 Christophe Chesneau , Salima El Kolei , Junke Kou , Fabien Navarro

We consider the nonparametric estimation of an S-shaped regression function. The least squares estimator provides a very natural, tuning-free approach, but results in a non-convex optimisation problem, since the inflection point is unknown.…

Methodology · Statistics 2024-12-17 Oliver Y. Feng , Yining Chen , Qiyang Han , Raymond J. Carroll , Richard J. Samworth

We study the adaptive minimax estimation of non-linear integral functionals of a density and extend the results obtained for linear and quadratic functionals to general functionals. The typical rate optimal non-adaptive minimax estimators…

Statistics Theory · Mathematics 2016-01-12 Rajarshi Mukherjee , Eric Tchetgen Tchetgen , James Robins

The aim of this paper is to discuss new results concerning some kinds of parametric extended entropies and divergences. As a result of our studies for mathematical properties on entropy and divergence, we give new bounds for the Tsallis…

Information Theory · Computer Science 2019-07-24 Shigeru Furuichi , Nicuşor Minculete

We provide general adaptive upper bounds for estimating nonparametric functionals based on second order U-statistics arising from finite dimensional approximation of the infinite dimensional models. We then provide examples of functionals…

Statistics Theory · Mathematics 2021-06-07 Lin Liu , Rajarshi Mukherjee , James Robins , Eric Tchetgen Tchetgen

Estimating density functionals of analog sources is an important problem in statistical signal processing and information theory. Traditionally, estimating these quantities requires either making parametric assumptions about the underlying…

Information Theory · Computer Science 2017-05-19 Alan Wisler , Kevin Moon , Visar Berisha

R\'enyi divergences play a pivotal role in information theory, statistics, and machine learning. While several estimators of these divergences have been proposed in the literature with their consistency properties established and minimax…

Information Theory · Computer Science 2025-09-12 Sreejith Sreekumar , Kengo Kato

Asymptotic properties of three estimators of probability density function of sample maximum $f_{(m)}:=mfF^{m-1}$ are derived, where $m$ is a function of sample size $n$. One of the estimators is the parametrically fitted by the…

Statistics Theory · Mathematics 2022-06-13 Taku Moriyama

Statistical divergences (SDs), which quantify the dissimilarity between probability distributions, are a basic constituent of statistical inference and machine learning. A modern method for estimating those divergences relies on…

Statistics Theory · Mathematics 2022-03-30 Sreejith Sreekumar , Ziv Goldfeld

The subject of this paper is the problem of nonparametric estimation of a continuous distribution function from observations with measurement errors. We study minimax complexity of this problem when unknown distribution has a density…

Statistics Theory · Mathematics 2012-02-27 I. Dattner , A. Goldenshluger , A. Juditsky

Estimating the score, i.e., the gradient of log density function, from a set of samples generated by an unknown distribution is a fundamental task in inference and learning of probabilistic models that involve flexible yet intractable…

Machine Learning · Statistics 2020-07-01 Yuhao Zhou , Jiaxin Shi , Jun Zhu

This paper provides a rigorous study of the nonparametric estimation of filaments or ridge lines of a probability density $f$. Points on the filament are considered as local extrema of the density when traversing the support of $f$ along…

Statistics Theory · Mathematics 2015-10-27 Wanli Qiao , Wolfgang Polonik

We consider settings where data are available on a nonparametric function and various partial derivatives. Such circumstances arise in practice, for example in the joint estimation of cost and input functions in economics. We show that when…

Statistics Theory · Mathematics 2009-09-29 Peter Hall , Adonis Yatchew

Many economic parameters are identified by ``thin sets'' (submanifolds with Lebesgue measure zero) and hence difficult to recover from data in an ambient space. This paper provides a unified theory for estimation and inference of such…

Econometrics · Economics 2026-03-09 Xiaohong Chen , Wayne Yuan Gao

It is often of interest to assess whether a function-valued statistical parameter, such as a density function or a mean regression function, is equal to any function in a class of candidate null parameters. This can be framed as a…

Methodology · Statistics 2023-06-14 Aaron Hudson

This paper tackles the issue of real-time parametric estimation of a wide class of probability density functions from limited datasets. This type of estimation addresses recent applications that require joint sensing and actuation. The…

Information Theory · Computer Science 2022-03-21 Ahmad A. Masoud

Estimators of doubly robust functionals typically rely on estimating two complex nuisance functions, such as the propensity score and conditional outcome mean for the average treatment effect functional. We consider the problem of how to…

Statistics Theory · Mathematics 2026-03-10 Sean McGrath , Rajarshi Mukherjee

Motivated by modeling and analysis of mass-spectrometry data, a semi- and nonparametric model is proposed that consists of a linear parametric component for individual location and scale and a nonparametric regression function for the…

Methodology · Statistics 2013-05-08 Weiping Ma , Yang Feng , Kani Chen , Zhiliang Ying

This paper is concerned with the estimation of the partial derivatives of a probability density function of directional data on the $d$-dimensional torus within the local thresholding framework. The estimators here introduced are built by…

Statistics Theory · Mathematics 2023-05-11 Claudio Durastanti , Nicola Turchi

This Note presents original rates of convergence for the deconvolution problem. We assume that both the estimated density and noise density are supersmooth and we compute the risk for two kinds of estimators.

Statistics Theory · Mathematics 2009-09-29 Claire Lacour