Some Statistical Problems with High Dimensional Financial data

TL;DR

This paper discusses the challenges of applying standard statistical methods to high-dimensional financial data and explores modifications and algorithms for covariance estimation, regression, PCA, testing, and classification.

Contribution

It introduces new modifications and fast algorithms for statistical techniques tailored to high-dimensional financial datasets.

Findings

Improved covariance matrix estimation methods

Fast algorithms for high-dimensional regression and PCA

Enhanced multiple testing and classification procedures

Abstract

For high dimensional data, some of the standard statistical techniques do not work well. So modification or further development of statistical methods are necessary. In this paper, we explore these modifications. We start with the important problem of estimating high dimensional covariance matrix. Then we explore some of the important statistical techniques such as high dimensional regression, principal component analysis, multiple testing problems and classification. We describe some of the fast algorithms that can be readily applied in practice.