Research Interests

In the study of random processes, dependence plays a fundamental role. By interpreting random processes as physical systems, I introduce physical dependence coefficients that quantify the
degree of dependence of outputs on inputs. Such dependence measures are related to the nonlinear system theory and riskmetrics. They provide a new framework for the study of random processes and shed new light on a variety of problems including estimation of linear models with dependent errors, nonparametric inference of time series, representations of sample quantiles, bootstrap for time series, spectral estimation among others. This work is published at Wu (October, 2005): Nonlinear system theory: Another look at dependence, Proceedings of the National Academy of Sciences.

I am currently interested in estimating covariance matrices of temporally observed series. The latter problem is quite important in the study of functional and longitudinal data. On the other hand, however, this problem is notoriously difficult since (i) one needs to estimate as many as n(n+1)/2 unknowns for a covariance matrix and (ii) a covariance matrix is intrinsically positive definite if the underlying random vector is linearly independent. This work is joint with Mohsen Pourahmadi.

Last update: 3/07

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