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We introduce and study a family of robust estimators for the functional logistic regression model whose robustness automatically adapts to the data thereby leading to estimators with high efficiency in clean data and a high degree of…

Methodology · Statistics 2023-05-03 Ioannis Kalogridis

We study the functional linear regression model with a scalar response and a Hilbert space-valued predictor, a canonical example of an ill-posed inverse problem. We show that the functional partial least squares (PLS) estimator attains…

Statistics Theory · Mathematics 2025-05-08 Andrii Babii , Marine Carrasco , Idriss Tsafack

This paper continues the research started in \cite{LW16}. In the framework of the convolution structure density model on $\bR^d$, we address the problem of adaptive minimax estimation with $\bL_p$--loss over the scale of anisotropic…

Statistics Theory · Mathematics 2017-04-17 Oleg Lepski , Thomas Willer

This paper considers adaptive, minimax estimation of a quadratic functional in a nonparametric instrumental variables (NPIV) model, which is an important problem in optimal estimation of a nonlinear functional of an ill-posed inverse…

Statistics Theory · Mathematics 2022-02-10 Christoph Breunig , Xiaohong Chen

Observations which are realizations from some continuous process are frequent in sciences, engineering, economics, and other fields. We consider linear models, with possible random effects, where the responses are random functions in a…

Statistics Theory · Mathematics 2016-11-30 Giacomo Aletti , Caterina May , Chiara Tommasi

We consider the non-parametric Poisson regression problem where the integer valued response $Y$ is the realization of a Poisson random variable with parameter $\lambda(X)$. The aim is to estimate the functional parameter $\lambda$ from…

Statistics Theory · Mathematics 2018-05-14 Martin Kroll

We propose an estimation procedure for linear functionals based on Gaussian model selection techniques. We show that the procedure is adaptive, and we give a non asymptotic oracle inequality for the risk of the selected estimator with…

Statistics Theory · Mathematics 2008-10-27 Béatrice Laurent , Carenne Ludeña , Clémentine Prieur

Functional logistic regression is a popular model to capture a linear relationship between binary response and functional predictor variables. However, many methods used for parameter estimation in functional logistic regression are…

Methodology · Statistics 2025-10-15 Berkay Akturk , Ufuk Beyaztas , Han Lin Shang

Conditional estimation given specific covariate values (i.e., local conditional estimation or functional estimation) is ubiquitously useful with applications in engineering, social and natural sciences. Existing data-driven non-parametric…

Machine Learning · Statistics 2020-10-13 Viet Anh Nguyen , Fan Zhang , Jose Blanchet , Erick Delage , Yinyu Ye

A theory of superefficiency and adaptation is developed under flexible performance measures which give a multiresolution view of risk and bridge the gap between pointwise and global estimation. This theory provides a useful benchmark for…

Statistics Theory · Mathematics 2007-06-13 T. Tony Cai , Mark G. Low

In the present paper we consider the problem of estimating a periodic $(r+1)$-dimensional function $f$ based on observations from its noisy convolution. We construct a wavelet estimator of $f$, derive minimax lower bounds for the $L^2$-risk…

Statistics Theory · Mathematics 2013-05-24 Rida Benhaddou , Marianna Pensky , Dominique Picard

We consider the problem of estimating the value of a linear functional 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…

Statistics Theory · Mathematics 2009-02-13 Christoph Breunig , Jan Johannes

This paper deals with robust marginal estimation under a general regression model when missing data occur in the response and also in some of covariates. The target is a marginal location parameter which is given through an $M-$functional.…

Functional data analysis is a fast evolving branch of modern statistics and the functional linear model has become popular in recent years. However, most estimation methods for this model rely on generalized least squares procedures and…

Methodology · Statistics 2020-06-24 Ioannis Kalogridis , Stefan Van Aelst

Functional quadratic regression models postulate a polynomial relationship between a scalar response rather than a linear one. As in functional linear regression, vertical and specially high-leverage outliers may affect the classical…

Methodology · Statistics 2023-05-30 Graciela Boente , Daniela Parada

For nonparametric regression with one-sided errors and a boundary curve model for Poisson point processes we consider the problem of efficient estimation for linear functionals. The minimax optimal rate is obtained by an unbiased estimation…

Statistics Theory · Mathematics 2015-09-25 Markus Reiß , Leonie Selk

We consider the nonparametric estimation problem of time-dependent multivariate functions observed in a presence of additive cylindrical Gaussian white noise of a small intensity. We derive minimax lower bounds for the $L^2$-risk in the…

Statistics Theory · Mathematics 2012-11-02 Jérémie Bigot , Theofanis Sapatinas

This paper deals with the nonparametric estimation in heteroscedastic regression $ Y_i=f(X_i)+\xi_i, \: i=1,...,n $, with incomplete information, i.e. each real random variable $ \xi_i $ has a density $ g_{i} $ which is unknown to the…

Statistics Theory · Mathematics 2011-05-10 Michaël Chichignoud

We construct an unbiased estimator for function value evaluated at the solution of a partial differential equation with random coefficients. We show that the variance and expected computational cost of our estimator are finite and our…

Probability · Mathematics 2019-04-23 Jose Blanchet , Fengpei Li , Xiaoou Li

This paper deals with estimation with functional covariates. More precisely, we aim at estimating the regression function $m$ of a continuous outcome $Y$ against a standard Wiener coprocess $W$. Following Cadre and Truquet (2015) and Cadre,…

Statistics Theory · Mathematics 2020-11-23 Karine Bertin , Nicolas Klutchnikoff