DeepAI AI Chat
Log In Sign Up

Quasi-parametric rates for Sparse Multivariate Functional Principal Components Analysis

12/19/2022
by   Ryad Belhakem, et al.
0

This work aims to give non-asymptotic results for estimating the first principal component of a multivariate random process. We first define the covariance function and the covariance operator in the multivariate case. We then define a projection operator. This operator can be seen as a reconstruction step from the raw data in the functional data analysis context. Next, we show that the eigenelements can be expressed as the solution to an optimization problem, and we introduce the LASSO variant of this optimization problem and the associated plugin estimator. Finally, we assess the estimator's accuracy. We establish a minimax lower bound on the mean square reconstruction error of the eigenelement, which proves that the procedure has an optimal variance in the minimax sense.

READ FULL TEXT

page 1

page 2

page 3

page 4

10/25/2021

Minimax estimation of Functional Principal Components from noisy discretized functional data

Functional Principal Component Analysis is a reference method for dimens...
03/01/2022

Adaptive nonparametric estimation in the functional linear model with functional output

In this paper, we consider a functional linear regression model, where b...
09/10/2020

Non-asymptotic Optimal Prediction Error for RKHS-based Partially Functional Linear Models

Under the framework of reproducing kernel Hilbert space (RKHS), we consi...
12/03/2018

Fast Covariance Estimation for Multivariate Sparse Functional Data

Covariance estimation is essential yet underdeveloped for analyzing mult...
12/07/2018

Principal components analysis of regularly varying functions

The paper is concerned with asymptotic properties of the principal compo...
10/27/2017

On the Optimal Reconstruction of Partially Observed Functional Data

We propose a new reconstruction operator that aims to recover the missin...
12/25/2017

Robust functional estimation in the multivariate partial linear model

We consider the problem of adaptive estimation of the functional compone...