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Related papers: Recovering Covariance from Functional Fragments

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We consider nonparametric estimation of the mean and covariance functions for functional/longitudinal data. Strong uniform convergence rates are developed for estimators that are local-linear smoothers. Our results are obtained in a unified…

Statistics Theory · Mathematics 2012-11-12 Yehua Li , Tailen Hsing

We study the semiparametric efficient estimation of a class of linear functionals in settings where a complete multivariate dataset is supplemented by additional datasets recording subsets of the variables of interest. These datasets are…

Statistics Theory · Mathematics 2025-06-19 Thomas B. Berrett

For covariance test in functional data analysis, existing methods are developed only for fully observed curves, whereas in practice, trajectories are typically observed discretely and with noise. To bridge this gap, we employ a…

Methodology · Statistics 2026-04-20 Yang Zhou , Jin Yang , Fang Yao

This paper examines the problem of nonparametric testing for the no-effect of a random covariate (or predictor) on a functional response. This means testing whether the conditional expectation of the response given the covariate is almost…

Statistics Theory · Mathematics 2014-11-25 Valentin Patilea , Cesar Sanchez-Sellero , Matthieu Saumard

Functional linear regression is an important topic in functional data analysis. It is commonly assumed that samples of the functional predictor are independent realizations of an underlying stochastic process, and are observed over a grid…

Methodology · Statistics 2020-09-15 Cheng Chen , Shaojun Guo , Xinghao Qiao

We consider the problem of recovering low-rank matrices from random rank-one measurements, which spans numerous applications including covariance sketching, phase retrieval, quantum state tomography, and learning shallow polynomial neural…

Information Theory · Computer Science 2018-12-04 Yuanxin Li , Cong Ma , Yuxin Chen , Yuejie Chi

We consider nonparametric regression with functional covariates, that is, they are elements of an infinite-dimensional Hilbert space. A locally polynomial estimator is constructed, where an orthonormal basis and various tuning parameters…

Statistics Theory · Mathematics 2025-04-09 Moritz Jirak , Alois Kneip , Alexander Meister , Mario Pahl

In this paper, a shrinkage estimator for the population mean is proposed under known quadratic loss functions with unknown covariance matrices. The new estimator is non-parametric in the sense that it does not assume a specific parametric…

Methodology · Statistics 2014-11-07 Cheng Wang , Tiejun Tong , Longbing Cao , Baiqi Miao

We consider the problem of recovering of continuous multi-dimensional functions from the noisy observations over the regular grid. Our focus is at the adaptive estimation in the case when the function can be well recovered using a linear…

Statistics Theory · Mathematics 2009-03-06 Anatoli Iouditski , Arkadii S. Nemirovski

This paper studies the problem of nonparametric testing for the effect of a random functional covariate on a real-valued error term. The covariate takes values in $L^2[0,1]$, the Hilbert space of the square-integrable real-valued functions…

Statistics Theory · Mathematics 2012-05-28 Valentin Patilea , Cesar Sanchez-Sellero , Matthieu Saumard

We study parameter estimation and asymptotic inference for sparse nonlinear regression. More specifically, we assume the data are given by $y = f( x^\top \beta^* ) + \epsilon$, where $f$ is nonlinear. To recover $\beta^*$, we propose an…

Machine Learning · Statistics 2015-11-17 Zhuoran Yang , Zhaoran Wang , Han Liu , Yonina C. Eldar , Tong Zhang

The non-parametric estimation of covariance lies at the heart of functional data analysis, whether for curve or surface-valued data. The case of a two-dimensional domain poses both statistical and computational challenges, which are…

Statistics Theory · Mathematics 2022-01-19 Tomas Masak , Soham Sarkar , Victor M. Panaretos

Nonparametric estimators for the mean and the covariance functions of functional data are proposed. The setup covers a wide range of practical situations. The random trajectories are, not necessarily differentiable, have unknown regularity,…

Statistics Theory · Mathematics 2025-02-13 Steven Golovkine , Nicolas Klutchnikoff , Valentin Patilea

The goal of this paper is to provide some tools for nonparametric estimation and inference in psychological and economic experiments. We consider an experimental framework in which each of $n$subjects provides $T$ responses to a vector of…

Econometrics · Economics 2019-12-10 Raffaello Seri , Samuele Centorrino , Michele Bernasconi

Motivated by recent work involving the analysis of leveraging spatial correlations in sparsified mean estimation, we present a novel procedure for constructing covariance estimator. The proposed Random-knots (Random-knots-Spatial) and…

Methodology · Statistics 2025-11-25 Sijie Zheng , Fandong Meng , Jie Zhou

In spatio-temporal analysis, we often record data at specific time intervals but with varying spatial locations between these timepoints. We propose a conditional model to analyze such spatio-temporal data that accommodates the dependencies…

Methodology · Statistics 2026-04-03 Subhrajyoty Roy , Soudeep Deb , Sayar Karmakar , Rishideep Roy

This paper considers an estimation of semiparametric functional (varying)-coefficient quantile regression with spatial data. A general robust framework is developed that treats quantile regression for spatial data in a natural…

Statistics Theory · Mathematics 2014-02-06 Zudi Lu , Qingguo Tang , Longsheng Cheng

Regression models with functional responses and covariates constitute a powerful and increasingly important model class. However, regression with functional data poses well known and challenging problems of non-identifiability. This…

Methodology · Statistics 2016-02-22 Fabian Scheipl , Sonja Greven

Consider discrete time observations (X_{\ell\delta})_{1\leq \ell \leq n+1}$ of the process $X$ satisfying $dX_t= \sqrt{V_t} dB_t$, with $V_t$ a one-dimensional positive diffusion process independent of the Brownian motion $B$. For both the…

Methodology · Statistics 2007-12-25 Fabienne Comte , Valentine Genon-Catalot , Yves Rozenholc

We develop theory and methodology for the problem of nonparametric registration of functional data that have been subjected to random deformation (warping) of their time scale. The separation of this phase variation ("horizontal" variation)…

Methodology · Statistics 2020-08-21 Anirvan Chakraborty , Victor M. Panaretos