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When a parameter of interest is defined to be a nondifferentiable transform of a regular parameter, the parameter does not have an influence function, rendering the existing theory of semiparametric efficient estimation inapplicable.…

Statistics Theory · Mathematics 2022-01-06 Kyungchul Song

In the multidimensional setting, we consider the errors-in-variables model. We aim at estimating the unknown nonparametric multivariate regression function with errors in the covariates. We devise an adaptive estimator based on projection…

Statistics Theory · Mathematics 2016-01-13 Michaël Chichignoud , Van Ha Hoang , Thanh Mai Pham Ngoc , Vincent Rivoirard

We consider the problem of estimating the structural function in nonparametric instrumental regression, where in the presence of an instrument W a response Y is modeled in dependence of an endogenous explanatory variable Z. The proposed…

Statistics Theory · Mathematics 2015-03-13 Jan Johannes , Maik Schwarz

We investigate function estimation in nonparametric regression models with random design and heteroscedastic correlated noise. Adaptive properties of warped wavelet nonlinear approximations are studied over a wide range of Besov scales,…

Statistics Theory · Mathematics 2009-09-03 Rafał Kulik , Marc Raimondo

Multiresolution provides a fundamental tool based on the wavelet theory to build adaptive numerical schemes for Partial Differential Equations and time-adaptive meshes, allowing for error control. We have introduced this strategy before to…

Numerical Analysis · Mathematics 2021-05-31 Thomas Bellotti , Loïc Gouarin , Benjamin Graille , Marc Massot

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

Let $\{(X_i,Y_i)\}_{i\in \{1,..., n\}}$ be an i.i.d. sample from the random design regression model $Y=f(X)+\epsilon$ with $(X,Y)\in [0,1]\times [-M,M]$. In dealing with such a model, adaptation is naturally to be intended in terms of…

Statistics Theory · Mathematics 2008-01-23 Pierpaolo Brutti

This paper studies transfer learning for estimating the mean of random functions based on discretely sampled data, where, in addition to observations from the target distribution, auxiliary samples from similar but distinct source…

Statistics Theory · Mathematics 2024-03-29 T. Tony Cai , Dongwoo Kim , Hongming Pu

We consider the problem of adaptive inference on a regression function at a point under a multivariate nonparametric regression setting. The regression function belongs to a H\"older class and is assumed to be monotone with respect to some…

Statistics Theory · Mathematics 2020-12-01 Koohyun Kwon , Soonwoo Kwon

This paper reviews recent developments in fundamental limits and optimal algorithms for change point analysis. We focus on minimax optimal rates in change point detection and localisation, in both parametric and nonparametric models. We…

Statistics Theory · Mathematics 2020-11-04 Yi Yu

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 study optimal procedures for estimating a linear functional based on observational data. In many problems of this kind, a widely used assumption is strict overlap, i.e., uniform boundedness of the importance ratio, which measures how…

Statistics Theory · Mathematics 2023-01-18 Wenlong Mou , Peng Ding , Martin J. Wainwright , Peter L. Bartlett

Block coordinate descent is an optimization paradigm that iteratively updates one block of variables at a time, making it quite amenable to big data applications due to its scalability and performance. Its convergence behavior has been…

Optimization and Control · Mathematics 2023-10-13 Liangzu Peng , René Vidal

Achieving ultimate bounds in estimation processes is the main objective of quantum metrology. In this context, several problems require measurement of multiple parameters by employing only a limited amount of resources. To this end,…

Adaptive bandwidth selection is a fundamental challenge in nonparametric regression. This paper introduces a new bandwidth selection procedure inspired by the optimality criteria for $\ell_0$-penalized regression. Although similar in spirit…

Machine Learning · Statistics 2025-05-21 Sabyasachi Chatterjee , Subhajit Goswami , Soumendu Sundar Mukherjee

The nonparametric volatility estimation problem of a scalar diffusion process observed at equidistant time points is addressed. Using the spectral representation of the volatility in terms of the invariant density and an eigenpair of the…

Applications · Statistics 2016-04-01 Jakub Chorowski

We consider a linear model where the coefficients - intercept and slopes - are random with a law in a nonparametric class and independent from the regressors. Identification often requires the regressors to have a support which is the whole…

Statistics Theory · Mathematics 2020-06-22 Christophe Gaillac , Eric Gautier

We construct estimators for the parameters of a parabolic SPDE with one spatial dimension based on discrete observations of a solution in time and space on a bounded domain. We establish central limit theorems for a high-frequency…

Statistics Theory · Mathematics 2025-04-23 Markus Bibinger , Patrick Bossert

Local dependence random graph models are a class of block models for network data which allow for dependence among edges under a local dependence assumption defined around the block structure of the network. Since being introduced by…

Statistics Theory · Mathematics 2025-01-06 Jonathan R. Stewart

Estimating linear, mean-square continuous functionals is a pivotal challenge in statistics. In high-dimensional contexts, this estimation is often performed under the assumption of exact model sparsity, meaning that only a small number of…

Statistics Theory · Mathematics 2025-08-04 Jelena Bradic , Victor Chernozhukov , Whitney K. Newey , Yinchu Zhu