Abstract

The factor models are powerful tools for uncovering patterns of similar

ity or co-movement among individuals, and they have been successfully applied

in the fields of finance and biology. However, the classical approximate factor

model encounters limitations when dealing with small sample sizes.

To overcome this challenge, we leverage auxiliary network information and propose a

novel joint quasi-maximum likelihood estimation, which can use the network information flexibly and allow network heterogeneity. The theoretical properties of

these estimators are rigorously established. We obtain a new convergence rate,

which is faster than the rate of classical maximum likelihood estimators when

the sample size is small. Numerous numerical studies have been conducted to

evaluate the performance of the proposed methods.

Information

Preprint No.SS-2024-0170
Manuscript IDSS-2024-0170
Complete AuthorsYuzhou Zhao, Xinyan Fan, Bo Zhang
Corresponding AuthorsXinyan Fan
Emails1031820039@qq.com

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Acknowledgments

This work is supported by National natural Science Foundation of China

(72271232, 71873137, 12201626), the MOE Project of Key Research Institute of Humanities and Social Sciences (22JJD110001), and Public Com-

puting Cloud of Renmin University of China.

Supplementary Materials

The Supplementary Material consists of ten sections (S.1–S.10). Section

S.1 provides a more general form of Theorem 3. Section S.2 introduces

some useful notations and lemmas that are used to prove the theoretical

properties in Section 3. Sections S.3–S.7 present the proofs of Theorems

1, 2, S.1 and 3, 4, and Proposition 1, respectively. Section S.8 provides

additional algorithmic details. Section S.9 details the comparison methods.

Section S.10 presents additional simulation results.

Supplementary materials are available for download.