Abstract

We consider an m×n matrix network data with m network nodes and n

dimensional responses for each node, where both m and n can diverge to infinity.

The heterogeneity of network nodal influence is addressed by different influence

parameters of each node, which are expressed through high-dimensional responses

using a specific link function. By allowing heterogeneous error variances, we propose a response-assisted network influence model to integrate information of the

matrix response variable and network structures across both m network nodes

and n dimensions of responses. Since the traditional maximum likelihood estimator is invalid in this case, we build an “optimal” generalized method of moments

estimator, to avoid estimating unknown error variances by restricting the diagonal of weighting matrix in quadratic moments. The consistency and asymptotic

normality of the estimator are established. We have also developed a homogeneity test to examine the influence heterogeneity and presented simulations and an

empirical study of fund and stock to demonstrate the model’s utility.

Information

Preprint No.SS-2024-0283
Manuscript IDSS-2024-0283
Complete AuthorsDongxue Zhang, Wei Lan, Danyang Huang, Huazhen Lin
Corresponding AuthorsDanyang Huang
Emailsdyhuang89@126.com

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Acknowledgments

Lan’s research was supported by the National Key R&D Program of China

(2022YFA1003702), the National Natural Science Foundation of China (72422020,

72333001, 12171395 and 71991472) and the Joint Lab of Data Science and

Business Intelligence at Southwestern University of Finance and Economics.

Lin’s research was supported by the National Key R&D Program of China

(2022YFA1003702) and the National Natural Science Foundation of China

(12426309). Huang’s research was supported by the National Natural Science Foundation of China (72471230), the National Key R&D Program of

China (2023YFC3304701), the Beijing Social Science Fund(23GLA008), the

MOE Project of Key Research Institute of Humanities and Social Sciences

(grant 22JJD110001) and Public Computing Cloud, Big Data and Responsible Artificial Intelligence for National Governance, Renmin University of

China. Zhang’s Research was supported by the Graduate Representative

Achievement Cultivation Project of Southwestern University of Finance and

Economics (JGS2024106).

Supplementary Materials

The online Supplementary Material includes six sections. Section S1 discusses the invalidity of ML estimation method. Section S2 gives the detailed

interpretation of Condition (C4). Section S3 presents the proofs of Theorems. Section S4 introduces a novel link function test to check the adequacy

of the pre-specified link function. Section S5 provides additional simulation

studies and empirical studies. Section S6 illustrates the details of variance

designs V1 and V2.

Supplementary materials are available for download.