19 June 2014

Thomas Mikosch receives DFF grant


Professor Thomas Mikosch has received a grant of DKK 1,902,451 from the The Danish Council for Independent Research for the project "Large random matrices with heavy tails and dependence."

Thomas Mikosch

Professor Thomas Mikosch

"The Danish Council for Independent Research received this year 1,244 applications in all academic fields, underlining the extremely fierce competition there is about DFF funds," said council chairman Professor Peter Munk Christiansen. There are given a total of 181 research grants.

DFF Natural Sciences has received 347 applications and awarded 52 grants for a total amount of 163 million DKK. One of the appropriations is allocated to Thomas Mikosch, professor at the Department for Mathematical Sciences.

Thomas Mikosch got his Master degree in Mathematics from TU Dresden (1981), defended his PhD in Probability Theory at St. Petersburg University (1984), and his Habilitation at TU Dresden (1990). Before he joined MATH/UCPH on 1 January 2001, he worked at TU Dresden, ETH Zürich, ISOR Wellington and RUG Groningen.

In his project description Mikosch writes:

"In the last 10 years large amounts of data have been collected throughout the world, especially in the context of medical studies (eg. genetic code), finance (high frequency data), climate data, Internet connections (Google), etc. These data (time series) are often high-dimensional and their dimensions may be greater than the number of data in the sample. Therefore, it is necessary to reduce the data to lower dimensions, ie. we try to extract the most important information from them.

One of the mathematical methods to reduce the dimension is Principal Component Analysis (PCA). The idea is to reduce the dimension using the eigenvalues, which is the basis for many high dimensional models. The task is to find out which of these eigenvalues are the largest (most important). The project will examine the distribution of the largest eigenvalues of large random matrices.

These time series have "heavy tails", ie. their values can be extremely large. For example, a stock market index from one of the major exchanges in the world where every listed company has a price. We observe the daily rates, which generate high dimensional time series (eg. the 500 dimensional S&P 500 in USA) and are interested in measuring the dependence between the different prices."