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Asymptotic in the Ordered Networks with a Noisy Degree Sequence

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Abstract

In the case of the differential privacy under the Laplace mechanism, the asymptotic properties of parameter estimators have been derived in some special network models with common binary values, but the asymptotic properties in network models with the ordered values are lacking. In this paper, the authors release the degree sequences of the ordered networks under a general noisy mechanism with the discrete Laplace mechanism as a special case. The authors establish the asymptotic result including the consistency and asymptotical normality of the parameter estimator when the number of parameters goes to infinity. Simulations and a real data example are provided to illustrate asymptotic results.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, South-Central University for Nationalities, Wuhan, 430074, China

    Jing Luo

  2. Department of Statistics, Zhongnan University of Economics and Law, Wuhan, 430073, China

    Hong Qin

Authors
  1. Jing Luo
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  2. Hong Qin
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Corresponding authors

Correspondence to Jing Luo or Hong Qin.

Additional information

Luo’s research is partially supported by the National Natural Science Foundation of China under Grant No. 11801576 and the National Statistical Science Research Project of China under Grant No. 2019LY59, and Qin’s research is partially supported by the National Natural Science Foundation of China under Grant No. 11871237.

This paper was recommended for publication by Editor TANG Niansheng.

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Luo, J., Qin, H. Asymptotic in the Ordered Networks with a Noisy Degree Sequence. J Syst Sci Complex 35, 1137–1153 (2022). https://doi.org/10.1007/s11424-021-0248-4

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  • DOI: https://doi.org/10.1007/s11424-021-0248-4

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