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High-dimensional group inference is an essential part of statistical methods for analysing complex data sets, including hierarchical testing, tests of interaction, detection of heterogeneous treatment effects and inference for local…

Methodology · Statistics 2020-12-01 Zijian Guo , Claude Renaux , Peter Bühlmann , T. Tony Cai

We propose a general method for constructing confidence intervals and statistical tests for single or low-dimensional components of a large parameter vector in a high-dimensional model. It can be easily adjusted for multiplicity taking…

Statistics Theory · Mathematics 2014-06-24 Sara van de Geer , Peter Bühlmann , Ya'acov Ritov , Ruben Dezeure

We study a functional linear regression model that deals with functional responses and allows for both functional covariates and high-dimensional vector covariates. The proposed model is flexible and nests several functional regression…

Statistics Theory · Mathematics 2022-08-24 Daren Wang , Zifeng Zhao , Yi Yu , Rebecca Willett

In this paper, we consider regression models with a Hilbert-space-valued predictor and a scalar response, where the response depends on the predictor only through a finite number of projections. The linear subspace spanned by these…

Statistics Theory · Mathematics 2010-11-12 Yehua Li , Tailen Hsing

In this paper, we propose methods for functional predictor selection and the estimation of smooth functional coefficients simultaneously in a scalar-on-function regression problem under high-dimensional multivariate functional data setting.…

Methodology · Statistics 2022-05-04 Ali Mahzarnia , Jun Song

We propose a methodology for testing linear hypothesis in high-dimensional linear models. The proposed test does not impose any restriction on the size of the model, i.e. model sparsity or the loading vector representing the hypothesis.…

Methodology · Statistics 2019-07-09 Yinchu Zhu , Jelena Bradic

We develop methodology for testing hypotheses regarding the slope function in functional linear regression for time series via a reproducing kernel Hilbert space approach. In contrast to most of the literature, which considers tests for the…

Statistics Theory · Mathematics 2022-02-17 Holger Dette , Jiajun Tang

We propose an extreme dimension reduction method extending the Extreme-PLS approach to the case where the covariate lies in a possibly infinite-dimensional Hilbert space. The ideas are partly borrowed from both Partial Least-Squares and…

Statistics Theory · Mathematics 2026-01-01 Stéphane Girard , Cambyse Pakzad

The concept of hypocoercivity for linear evolution equations with dissipation is discussed and equivalent characterizations that were developed for the finite-dimensional case are extended to separable Hilbert spaces. Using the concept of a…

Dynamical Systems · Mathematics 2025-01-30 Franz Achleitner , Anton Arnold , Volker Mehrmann , Eduard A. Nigsch

This paper aims to front with dimensionality reduction in regression setting when the predictors are a mixture of functional variable and high-dimensional vector. A flexible model, combining both sparse linear ideas together with…

Statistics Theory · Mathematics 2024-01-29 Silvia Novo , Germán Aneiros , Philippe Vieu

This paper studies inference in the high-dimensional linear regression model with outliers. Sparsity constraints are imposed on the vector of coefficients of the covariates. The number of outliers can grow with the sample size while their…

Statistics Theory · Mathematics 2021-02-08 Jad Beyhum

Inference on the parametric part of a semiparametric model is no trivial task. If one approximates the infinite dimensional part of the semiparametric model by a parametric function, one obtains a parametric model that is in some sense…

Statistics Theory · Mathematics 2025-09-23 Adam Lee , Emil A. Stoltenberg , Per A. Mykland

We study a non linear regression model with functional data as inputs and scalar response. We propose a pointwise estimate of the regression function that maps a Hilbert space onto the real line by a local linear method. We provide the…

Statistics Theory · Mathematics 2013-02-20 Alain Berlinet , Abdallah Elamine , André Mas

We consider functional linear regression models where functional outcomes are associated with scalar predictors by coefficient functions with shape constraints, such as monotonicity and convexity, that apply to sub-domains of interest. To…

Methodology · Statistics 2025-05-09 Kyunghee Han , Yeonjoo Park , Soo-Young Kim

Consider estimation of the regression function based on a model with equidistant design and measurement errors generated from a fractional Gaussian noise process. In previous literature, this model has been heuristically linked to an…

Statistics Theory · Mathematics 2014-12-02 Johannes Schmidt-Hieber

This short technical report presents some learning theory results on vector-valued reproducing kernel Hilbert space (RKHS) regression, where the input space is allowed to be non-compact and the output space is a (possibly…

Machine Learning · Statistics 2022-02-17 Junhyunng Park , Krikamol Muandet

This paper deals with the Fisher-consistency, weak continuity and differentiability of estimating functionals corresponding to a class of both linear and nonlinear regression high breakdown M estimates, which includes S and MM estimates. A…

Statistics Theory · Mathematics 2012-11-26 María V. Fasano , Ricardo A. Maronna , Mariela Sued , Víctor J. Yohai

Let $X$ be a Bernoulli random variable with the success probability $p$. We are interested in tight bounds on $\mathbb{E}[f(X_1,X_2)]$, where $X_i=\mathbb{E}[X| \mathcal{F}_i]$ and $\mathcal{F}_i$ are some sigma-algebras. This problem is…

Probability · Mathematics 2024-05-28 Egor Kravchenko

We propose a robust inferential procedure for assessing uncertainties of parameter estimation in high-dimensional linear models, where the dimension $p$ can grow exponentially fast with the sample size $n$. Our method combines the…

Machine Learning · Statistics 2015-03-19 Tianqi Zhao , Mladen Kolar , Han Liu

Learning rates for least-squares regression are typically expressed in terms of $L_2$-norms. In this paper we extend these rates to norms stronger than the $L_2$-norm without requiring the regression function to be contained in the…

Machine Learning · Statistics 2020-10-27 Simon Fischer , Ingo Steinwart