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

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

doi:10.1109/TSP.2017.2691667

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

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

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Abstract

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 language	English
Article number	7893802
Pages (from-to)	3234-3246
Number of pages	13
Journal	IEEE Transactions on Signal Processing
Volume	65
Issue number	12
DOIs	https://doi.org/10.1109/TSP.2017.2691667
State	Published - Jun 15 2017

Keywords

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

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10.1109/TSP.2017.2691667

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title = "The β-Model-Maximum Likelihood, Cram{\'e}r-Rao Bounds, and Hypothesis Testing",

abstract = "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. Cram{\'e}r-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.",

keywords = "Cram{\'e}r-Rao bounds, dynamic social networks, hypothesis testing, random graphs, The β-model",

author = "Johan Wahlstr{\"o}m and Isaac Skog and Rosa, {Patricio S.La} and Peter H{\"a}ndel and Arye Nehorai",

note = "Funding Information: The work of A. Nehorai was supported by the Air Force Office of Scientific Research under Grant FA9550-11-1-0210. Publisher Copyright: {\textcopyright} 1991-2012 IEEE.",

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AU - Nehorai, Arye

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

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