2021/06/07 by Qiuping Wang, Wang, Qiuping
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Statistical Methods and Inference #Statistics Theory (math.ST) #math.ST #stat.TH
paper · pdf · doi:10.48550/arxiv.2106.03285
19 pages,2 figures,3 tables. arXiv admin note: substantial text overlap with arXiv:1609.04558 by other authors
arxiv created 2021/06/07 · openalex publication_date 2021/06/07 · arxiv updated 2021/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We are concerned here with unrestricted maximum likelihood estimation in a sparse p0 model with covariates for directed networks. The model has a density parameter ν, a 2n-dimensional node parameter \bsη and a fixed dimensional regression coefficient \bsγ of covariates. Previous studies focus on the restricted likelihood inference. When the number of nodes n goes to infinity, we derive the ℓ_∞-error between the maximum likelihood estimator (MLE) (\widehat\bsη, \widehat\bsγ) and its true value (\bsη, \bsγ). They are Op( (log n/n)1/2 ) for \widehat\bsη and Op( log n/n) for \widehat\bsγ, up to an additional factor. This explains the asymptotic bias phenomenon in the asymptotic normality of \widehat\bsγ in \citeYan-Jiang-Fienberg-Leng2018. Further, we derive the asymptotic normality of the MLE. Numerical studies and a data analysis demonstrate our theoretical findings.