Research Projects
Degree Growth and Index Estimation for Network Models
Project Overview
Preferential attachment is widely used to model power-law behavior of degree distributions in both directed and undirected networks. Statistical estimates of the marginal tail exponent of the power-law degree distribution often use the Hill estimator as one of the key summary statistics, even though no theoretical justification has been given. This project focuses on convergence of the empirical measure for degree sequences and proves the consistency of the Hill estimator.
T. Wang and S.I. Resnick. Consistency of Hill Estimators in a Linear Preferential Attachment Model. Extremes, 2018. DOI: 10.1007/s10687-018-0335-7.
T. Wang and S.I. Resnick. Degree Growth Rates and Index Estimation in a Directed Preferential Attachment Model. ArXiv e-prints: 1808.01637, 2018. Submitted.
Statistical Inferences for Network Models
Project Overview
Preferential attachment is an appealing edge generating mechanism for modeling social networks. We first consider methods for fitting a 5-parameter linear preferential model to network data under two data scenarios. However, there are often limitations in fitting parametric network models to data due to the complex nature of real-world networks. Then we propose a semi-parametric estimation approach by looking at only the nodes with large in- or out-degrees of the network. This method examines the tail behavior of both the marginal and joint degree distributions and is based on extreme value theory. We compare it with the existing parametric approaches and demonstrate how it can provide more robust estimates of parameters associated with the network when the data are corrupted or when the model is misspecified.
P. Wan, T. Wang, R.A. Davis and S.I. Resnick. Fitting the Linear Preferential Attachment Model. Electronic Journal of Statistics, 11(2):37383780, 2017.
P. Wan, T. Wang, R.A. Davis and S.I. Resnick. Are Extreme Value Estimation Methods Useful for Network Data? ArXiv e-prints: 1712.07166, 2017. Submitted.
Other Works
T. Wang and S.I. Resnick. Multivariate Regular Variation of Discrete Mass Functions with Applications to Preferential Attachment Networks. Methodology and Computing in Applied Probability, pages 1-14, 2016.
T. Wang and S.I. Resnick. Asymptotic Normality of In- and Out-Degree Counts in a Preferential Attachment Model. Stochastic Models, 33(2):229-255, 2017.
Y. Fan, P. Griffin, R.A. Maller, A. Szimayer and T. Wang. The Effects of Largest Claims and Excess of Loss Reinsurance on a Company's Ruin Time and Valuation. Risks, 5(1):3, 2017.
Working Paper
H. Drees, A. Janssen, T. Wang and S.I. Resnick. Threshold Selection by Distance Minimization. In preparation.
T. Wang and S.I. Resnick. Asymptotic Normality of the Hill Estimator in a Linear Preferential Attachment Model. In preparation.
Presentations
"Are Extreme Value Estimation Methods Useful for Network Data?" Contributed talk at Joint Statistics Meeting, July 2018, Vancouver, Canada.
"Consistency of Hill Estimators in a Linear Preferential Attachment Model". Contributed talk at Self-Similarity, Long-Range Dependence and Extreme, June 2018, BIRS-CMO, Oaxaca, Mexico.
"Consistency of Hill Estimators in a Linear Preferential Attachment Model". Contributed talk at 4th International Workshop on Statistical Modeling of Heavy-Tail Phenomena with Applications, June 2018, Suzhou, China.
"Multivariate Regular Variation of In- and Out-Degrees in Preferential Attachment Networks". Invited talk at Workshop on Levy processes and time series: in honour of Peter Brockwell and Ross Maller, September 2017, Ulm University, Germany.
"Multivariate Regular Variation of In- and Out-Degrees in Preferential Attachment Networks". Contributed talk at 10th Extreme Value Analysis Conference, June 2017, TU Delft, Netherlands.
"Asymptotic Normality of In- and Out-Degree Counts in a Preferential Attachment Model". Invited talk at New England Statistics Symposium, April 2017, University of Connecticut, Storrs, Connecticut, USA.
"Multivariate Regular Variation of Discrete Mass Functions with Applications to Preferential Attachment Networks". Poster presentation at Workshop on Dependence, Stability and Extremes, May 2016, Fields Institute, Toronto, Canada.
"Asymptotic Behavior of the Ruinous Jump in the General Levy Insurance Risk Model". Contributed talk at Kioloa Conference: From Random Walks to Levy Processes, January 2014, Australian National University, Canberra, Australia.
Teaching Experience
ENGRD2700 Basic Engineering Probability and Statistics: Lead Teaching Assistant, Cornell University, Ithaca, NY, Fall 2018.
ORIE5640 Statistics for Financial Engineering: Teaching Assistant, Cornell University, Ithaca, NY, Spring 2018.
ENGRD2700 Basic Engineering Probability and Statistics: Teaching Assistant, Cornell University, Ithaca, NY, Fall 2014.
STAT2008/6038 Regression Modeling: Tutor, Australian National University, Canberra, ACT, Australia, Spring 2012.
Academic Honors
Australian National University, University Medal in Statistics 2013.
Australian National University, Goldman Sachs J B Were Prize, 2013.
Australian National University, Colloge of Business and Economics Honors Scholarship, 2012.