# Asymptotic and bootstrap tests for the dimension of the non-Gaussian subspace

## TL;DR

This paper introduces asymptotic and bootstrap statistical tests to accurately determine the dimension of the non-Gaussian subspace in data, enhancing the effectiveness of non-Gaussian component analysis.

## Contribution

It develops new asymptotic and bootstrap testing procedures for the subspace dimension in non-Gaussian component analysis using FOBI.

## Key findings

- Tests perform well in simulations
- Bootstrap method improves accuracy in finite samples
- Provides reliable dimension estimation in practice

## Abstract

Dimension reduction is often a preliminary step in the analysis of large data sets. The so-called non-Gaussian component analysis searches for a projection onto the non-Gaussian part of the data, and it is then important to know the correct dimension of the non-Gaussian signal subspace. In this paper we develop asymptotic as well as bootstrap tests for the dimension based on the popular fourth order blind identification (FOBI) method.