Dimension estimation in PCA model using high-dimensional data augmentation

TL;DR

This paper introduces a high-dimensional PCA dimension estimation method that incorporates augmented noise variables, demonstrating consistency and improved performance over existing methods through theoretical analysis and simulations.

Contribution

It presents a novel high-dimensional augmentation approach for PCA dimension estimation, explaining its advantages and limitations compared to previous methods.

Findings

The proposed method is consistent in high-dimensional settings.

Augmentation improves estimation accuracy over existing methods.

Simulations confirm the method's superiority in various scenarios.

Abstract

We propose a modified, high-dimensional version of a recent dimension estimation procedure that determines the dimension via the introduction of augmented noise variables into the data. Our asymptotic results show that the proposal is consistent in wide high-dimensional scenarios, and further shed light on why the original method breaks down when the dimension of either the data or the augmentation becomes too large. Simulations are used to demonstrate the superiority of the proposal to competitors both under and outside of the theoretical model.