The main goals are the following:
- To achieve a quantitative understanding of the structure of multivariate and matrix variate distributions with applications to machine learning, finance, signal processing, among others;
- To elaborate data-driven methods for the estimation of high-dimensional optimal portfolios from viewpoints of both frequentist and Bayesian statistics;
- To develop new methods for making statistical inference on the mean vector, the regression coefficients, the covariance matrix, and the precision matrix in the high-dimensional setting;
- To improve the estimation of the parameters in high-dimensional volatility models;
- To establish the distributional properties of multiple testing procedures with dependent test statistics;
- To derive sequential procedures for detecting changes in the parameters of high-dimensional statistical models.
The obtained results were published in major statistical and financial journals, like The Annals of Statistics, Journal of Machine Learning Research, Journal of Business and Economic Statistics, IEEE Transactions on Signal Processing, Bayesian Analysis, Scandinavian Journal of Statistics, Journal of Multivariate Analysis, The European Journal of Operational Research, Journal of the Empirical Finance, Finance Research Letters, Computational Statistics and Data Analysis, Applied Mathematics and Computation, The European Journal of Finance, among others.
