**Orateur:** Esa OLLILA (Aalto University and Oulu University, Finland)

**Titre:** High-dimensional covariance matrix estimation with applications to microarray studies and portfolio optimization

**Résumé:**

We consider the problem of estimating a high-dimensional (HD) covariance matrix that can be applied in commonly occurring sparse data problems, i.e., when the sample size is smaller or not much larger than the dimensionality of the data, which is potentially very large. We develop a well-conditioned regularized sample covariance matrix (RSCM) estimator that is asymptotically optimal in the minimum mean squared error sense w.r.t. Frobenius metric under the assumption that the data samples follow an unspecified elliptically symmetric distribution. Asymptotically means that the number of observations and the number of variables grow large together. The proposed RSCM estimator has a simple explicit formula that is easy to compute and to interpret.

The proposed covariance estimator is then used in microarray data analysis (MDA) and portfolio optimization problem in finance. Microarray technology is a powerful approach for genomics research that allows monitoring the expression levels of tens of thousands of genes simultaneously. In MDA the task is to select differentially expressed genes, i.e., which genes influence the trait (e.g., a particular cancer), and to perform accurate classification (e.g., deciding to which cancer class a new sample belongs to). In portfolio optimization problem we use our estimator for optimally allocating the total wealth to a large number of assets, where optimality means that the risk (i.e., variance of portfolio returns) is minimized. Our analysis results on real microarray data and stock market data illustrate that the proposed approach is able to outperform the benchmark methods.

** Biography:** Esa Ollila (M’03) received the M.Sc. degree in mathematics from the University of Oulu, in 1998, Ph.D. degree in statistics with honors from the University of Jyvaskyla, in 2002, and the D.Sc. (Tech) degree with honors in signal processing from Aalto University, in 2010. From 2004 to 2007 he was a post-doctoral fellow and from August 2010 to May 2015 an Academy Research Fellow of the Academy of Finland. He has also been a Senior Lecturer at the University of Oulu. Currently, since June 2015, he is an Associate Professor of Signal Processing at Aalto University. He is also an adjunct Professor (statistics) of Oulu University. During the Fall-term 2001, he was a Visiting Researcher with the Department of Statistics, Pennsylvania State University, State College, PA while the academic year 2010-2011 he spent as a Visiting Post-doctoral Research Associate with the Department of Electrical Engineering, Princeton University, Princeton, NJ. His research interests focus on theory and methods of statistical signal processing, multivariate statistics and data science.