Statistics and Its Interface

Volume 15 (2022)

Number 3

Asymptotic in a class of network models with a difference private degree sequence

Pages: 383 – 397

DOI: https://dx.doi.org/10.4310/21-SII702

Authors

Jing Luo (Department of Mathematics and Statistics, South-Central University for Nationalities, Wuhan, China)

Hong Qin (Department of Statistics, Zhongnan University of Economics and Law, Wuhan, China)

Abstract

The asymptotic properties of parameter estimators with a difference private degree sequence have been derived in $\beta$‑model with common binary values, but the general asymptotic properties in network models are lacking. Therefore, we will establish the unified asymptotic result including the consistency and asymptotical normality of the parameter estimator in a class of network models with a difference private degree sequence. Simulations are provided to illustrate asymptotic results.

Keywords

asymptotic normality, consistency, network data, degree, differential privacy

2010 Mathematics Subject Classification

Primary 62E20. Secondary 62F12.

Full Text (PDF format)

Luo is partially supported by the National Natural Science Foundation of China (no. 11801576).

Qin is partially supported by the National Natural Science Foundation of China (no. 11871237).

Received 12 January 2021

Accepted 26 August 2021

Published 14 February 2022