Social network modelling provides plenty of data but realistic models for network growth must be simple if any mathematical results are expected. We have used preferential attachment (PA) models with a small number of parameters in an attempt to strike a balance between the mathematics and the statistical fitting. The PA models struggle to match the data but provide a context in which to test methods and analyse estimation techniques. Numerical summaries of network characteristics are often estimated using methods imported from classical statistics without real justification. For example, the Hill estimator coupled with a minimum distance threshold selection technique is commonly used. We discuss some attempts to justify and understand these estimation methods in the context of PA models. Without a model and its properties, there is no way to understand the limitation of estimation methods.
Professor Sidney Resnick joined the Cornell faculty in 1987 after nine years at Colorado State University, six years at Stanford University, and two years at the Technion, in Haifa, Israel. He has held visiting appointments at the University of Amsterdam and the Amsterdam Mathematics Center; the Australian National University and CSIRO, in Canberra, Australia; the Technion in Israel (as a Lady Davis Fellow); Sussex University, in Brighton, UK, Erasmus University Rotterdam, ETH Zurich, Department of Statistics, UNC, Chapel Hill; Columbia University; Samsi, Research Triangle Park, NC; Technical University Munich (as John Von Neuman Visiting Professor). Resnick is a fellow of the Institute of Mathematical Statistics, and while at Colorado State was an Oliver Pennock Distinguished Service Award winner. He is a founding associate editor of Annals of Applied Probability, and a current associate editor of Stochastic Models, Extremes, Stochastic Processes and their Applications and The Mathematical Scientist. He is a former associate editor of Journal of Applied Probability. He served a three-year term on the Council of the Institute of Mathematical Statistics and served on their ad hoc committee on electronic publishing. He is currently an editor for Birkhauser, Boston serving on the boards of the Progress in Probability and Progress in Probability and Its Applications series and also serves on the editorial board of the Springer series Operations Research and Financial Engineering. His BS is from Queens College, NYC and his PhD is from Purdue. Resnick concluded a five year term as Director of Cornell’s School of Operations Research and Information Engineering in June 2004. Professor Resnick has authored or coauthored 160 papers and four books.
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