Estimation for ultra-high dimensional factor model: a pivotal variable detection based approach

TL;DR

This paper introduces a novel two-stage method for estimating ultra-high dimensional factor models by detecting pivotal variables, improving efficiency under weaker assumptions, and demonstrating effectiveness through simulations and real data analysis.

Contribution

It proposes a new pivotal variable detection approach and a two-stage estimation procedure tailored for ultra-high dimensional factor models, addressing limitations of existing sparse covariance methods.

Findings

The method effectively detects pivotal variables in high-dimensional settings.

The two-stage approach improves estimation accuracy and efficiency.

Simulation and real data analyses validate the proposed method's performance.

Abstract

For factor model, the involved covariance matrix often has no row sparse structure because the common factors may lead some variables to strongly associate with many others. Under the ultra-high dimensional paradigm, this feature causes existing methods for sparse covariance matrix in the literature not directly applicable. In this paper, for general covariance matrix, a novel approach to detect these variables that is called the pivotal variables is suggested. Then, two-stage estimation procedures are proposed to handle ultra-high dimensionality in factor model. In these procedures, pivotal variable detection is performed as a screening step and then existing approaches are applied to refine the working model. The estimation efficiency can be promoted under weaker assumptions on the model structure. Simulations are conducted to examine the performance of the new method and a real dataset is analysed for illustration.