Nonparametric principal subspace regression

TL;DR

This paper introduces a flexible nonparametric principal subspace regression method that effectively captures smooth multivariate signals with covariates, outperforming traditional PCA and regression techniques.

Contribution

It proposes a novel two-step framework for nonparametric principal subspace regression, with theoretical guarantees and practical implementation procedures.

Findings

Demonstrates favorable finite-sample performance in simulations

Shows effectiveness on EEG data application

Provides theoretical properties of the framework

Abstract

In scientific applications, multivariate observations often come in tandem with temporal or spatial covariates, with which the underlying signals vary smoothly. The standard approaches such as principal component analysis and factor analysis neglect the smoothness of the data, while multivariate linear or nonparametric regression fail to leverage the correlation information among multivariate response variables. We propose a novel approach named nonparametric principal subspace regression to overcome these issues. By decoupling the model discrepancy, a simple and general two-step framework is introduced, which leaves much flexibility in choice of model fitting. We establish theoretical property of the general framework, and offer implementation procedures that fulfill requirements and enjoy the theoretical guarantee. We demonstrate the favorable finite-sample performance of the proposed method through simulations and a real data application from an electroencephalogram study.