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Asymptotic in the Ordered Networks with a Noisy Degree Sequence

LUO Jing1, QIN Hong2   

  1. 1. Department of Mathematics and Statistics, South-Central University for Nationalities, Wuhan 430074, China;2. Department of Statistics, Zhongnan University of Economics and Law, Wuhan 430073, China
  • Received:2020-10-09 Revised:2020-12-14 Published:2022-06-20
  • Supported by:
    This research was supported by the Major Program of National Natural Science Foundation of China under Grant Nos. 61690210 and 61690212, the National Natural Science Foundation of China under Grant No. 61333003, and also by the Science Center Program of the National Natural Science Foundation of China under Grant No. 62188101.

LUO Jing, QIN Hong. Asymptotic in the Ordered Networks with a Noisy Degree Sequence[J]. Journal of Systems Science and Complexity, 2022, 35(3): 1137-1153.

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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