Statistics and Stochastic Processes

In broad terms, the research carried out in this area focused mainly on stochastic and telecommunication networks, statistical inference on Internet networks, multivariate analysis, robust statistics, biostatistics, and quality control. In particular, we have investigated:

• Queues with correlated input traffic and correlated services of interest in communication networks;
• Stochastic networks where different classes of individuals move according to some routing policy, showing in particular that under some conditions on the parameters, in the limit, several stable equilibrium points;
• Analysis of multihop path reliability in Mobile Ad-hoc Networks (MANETs);
• Modeling of Internet traffic and estimation of Internet traffic from sampling traffic;
• Robust estimation and hypothesis testing in common principal components, and detection of influential observations in principal components and common principal components;
• Robust linear regression methods, with a R-package code, in genomic association studies;
• Robust feature selection and robust principal component for Internet traffic anomaly detection;
• Stochastic ordering of the performance of quality control charts for simultaneous schemes for the mean and covariance matrix of bivariate processes and misleading signals in simultaneous residual schemes for the
• Development of the new efficient applied methods and codes for maximum (or quasi-maximum) likelihood estimation of linear dynamic stochastic systems by using numerically stable Kalman filtering algorithms;
• New efficient applied methods and codes for the quasi-maximum likelihood estimation of financial time-series model estimation (GARCH and stochastic volatility models).

The research will focus on several areas of applied statistics and stochastic processes, including: multivariate analysis, quality control, robust statistics, mathematical finance, and stochastic and telecommunication networks. The research will be carried out in close connection with engineers and economists, and there will be emphasis in producing codes implementing the methods resulting from the research in widely used software packages like the R statistical package.