Homepage of Nestor Parolya

Dr. Nestor Parolya
Assistant professor
Mekelweg 4
2628 CD Delft
Phone: 015-2782515
Office: 36.HB 06.290
E-mail: n.parolya@tudelft.nl

What is the true relationship between the eigenvalues of the high-dimensional sample covariance matrix S_n with limiting spectral distribution (LSD) F and its population counterpart Sigma with LSD given by H if p/n ("dimension"/"sample size" ratio) tends to a constant c>0? Integral fixed point equation in terms of the corresponding Stieltjes transforms! In case Sigma=I the solution is the well-known Marchenko-Pastur law.
Toy example: let the true covariance matrix is equal to the identity matrix. How good the sample covariance matrix S_n estimates the true one in terms of its eigenvalues if dimension p=500 and the sample size n=1000? The picture says it all.
"Why should the same equation describe both the structure of an atomic nucleus and a sequence at the heart of number theory? And what do random matrices have to do with either of those realms? In recent years, the plot has thickened further, as random matrices have turned up in other unlikely places, such as games of solitaire, one-dimensional gases and chaotic quantum systems. Is it all just a cosmic coincidence, or is there something going on behind the scenes?" - Brian Hayes, The Spectrum Of Riemannium, American Scientist (2003)

I am working on the theory and applications of large random matrices. One of the most important application areas is high-dimensional statistics, which is dedicated to the estimation and inference of large covariance matrices, mean vectors and their functionals. The developed techniques can be successfully applied in finance and econometrics, esp. in estimation and optimization of large portfolios, forecasting of large dimensional time series and realized covariance matrices. Furthermore, because the optimal portfolios are mathematically equivalent to the minimum variance beamformers, the obtained results find their direct applications in statistical signal processing and wireless communications.

News feed

02/11/2021 Paper "Optimal shrinkage-based portfolio selection in high dimensions" is accepted for publication in Journal of Business and Economic Statistics . online first .
13/09/2021 New R package "DOSPortfolio: Dynamic Optimal Shrinkage Portfolio" published online by CRAN .
25/08/2021 Review article "Recent advances in shrinkage-based high-dimensional inference" accepted for publication in Journal of Multivariate Analysis . online first .
02/08/2021 First R package "HDShOP: High-Dimensional Shrinkage Optimal Portfolios" published online by CRAN .
03/06/2021 New preprint "Dynamic Shrinkage Estimation of the High-Dimensional Minimum-Variance Portfolio " available. Joint work with Taras Bodnar (Stockholm University) and Erik Thorsen (Stockholm University). arxiv.org .
04/04/2021 New preprint "Logarithmic law of large random correlation matrix" available. Joint work with Johannes Heiny (RUB) and Dorota Kurowicka (TUD) arxiv.org .
26/03/2021 paper "Sampling Distributions of Optimal Portfolio Weights and Characteristics in Small and Large Dimensions " accepted for publication in Random Matrices: Theory and Applications .
29/10/2020 paper "Statistical inference for the expected utility portfolio in high dimensions" accepted for publication in IEEE Transactions of Signal Processing .
23/09/2020 Book chapter "Spectral analysis of large reflexive generalized inverse and Moore-Penrose Inverse Matrices" of Recent Developments in Multivariate and Random Matrix Analysis is online
01/08/2020 PhD position "Statistical Integer Linear Programming in High Dimensions" announced. Deadline 01.09.2020.
17/08/2020 paper "Mean-variance efficiency of optimal power and logarithmic utility portfolios" is published in Mathematics and Financial Economics.
04/06/2020 paper "Bayesian mean-variance analysis: Optimal portfolio selection under parameter uncertainty" has recently been published online in Quantitative Finance
10/09/2019 received an award Wolfgang-Wetzel-Preis during statistical conference Statistical Week 2019 in Trier, Germany.
02/09/2019 paper "Bayesian inference of the multi-period optimal portfolio for an exponential utility " is accepted by Journal of Multivariate Analysis .
12/08/2019 paper "Testing for independence of large dimensional vectors" is published in The Annals of Statistics .
28/06/2019 paper "Tests for the weights of the global minimum variance portolio in a high-dimensional setting" is published in IEEE Transactions of Signal Processing .
25/04/2019 paper "CLTs for functionals of large covariance matrix and mean vector in matrix-variate location mixture of normal distributions" is published in Scandinavian Journal of Statistics .

Research interests

Large random matrices and high-dimensional statistics
Mathematical and statistical finance
Financial engineering and operations research

Short CV

04/2019 -       Assistant Professor of Statistics (tenure track), Delft University of Technology, Netherlands
2017 - 2018   Visiting Professor of Econometrics and Statistics, Heidelberg and Mannheim Universities, resp., Germany
2014 - 2019   Assistant Professor of Financial Econometrics, Leibniz University Hannover, Germany
2013 - 2014   PostDoc, Department of Statistics and Econometrics, Ruhr University Bochum, Germany
2010 - 2013   PhD in Economics with major in Statistics, Viadrina University, Germany
2005 - 2010   BSc. in Mathematics and MSc. in Statistics, University of Lviv, Ukraine