The β-Model-Maximum Likelihood, Cramér-Rao Bounds, and Hypothesis Testing

Johan Wahlström, Isaac Skog, Patricio S.La Rosa, Peter Händel, Arye Nehorai

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


We study the maximum-likelihood estimator in a setting where the dependent variable is a random graph and covariates are available on a graph level. The model generalizes the well-known β-model for random graphs by replacing the constant model parameters with regression functions. Cramér-Rao bounds are derived for special cases of the undirected β-model, the directed β-model, and the covariate-based β-model. The corresponding maximum-likelihood estimators are compared with the bounds by means of simulations. Moreover, examples are given on how to use the presented maximum-likelihood estimators to test for directionality and significance. Finally, the applicability of the model is demonstrated using temporal social network data describing communication among healthcare workers.

Original languageEnglish
Article number7893802
Pages (from-to)3234-3246
Number of pages13
JournalIEEE Transactions on Signal Processing
Issue number12
StatePublished - Jun 15 2017


  • Cramér-Rao bounds
  • dynamic social networks
  • hypothesis testing
  • random graphs
  • The β-model


Dive into the research topics of 'The β-Model-Maximum Likelihood, Cramér-Rao Bounds, and Hypothesis Testing'. Together they form a unique fingerprint.

Cite this