The Department of Statistics conducts research in several areas of statistics. These areas are presented below. Please visit the researchers´ personal presentations for more detailed information.
In financial statistics studies are conducted of optimal investment strategies under constraints and of dependencies between GARCH processes. In our studies we also extend beyond the Gaussian paradigm of error distribution in the financial and economic data models. The models are used to investigate the driving forces of market risks.
The department’s research in stochastic networks is focused on statistical models for social networks.
Active researchers: Krzysztof Nowicki
Part of the research in this field focuses on sample spaces with constraints, for instance correlation structures on simplices and models for circular data. Another part focuses on multivariate generalised linear models and multilevel models.
The department carries out applied research in biostatistics in collaboration with, inter alia, neurosurgeons, psychiatrists, paediatricians and dentists. It also conducts theoretical biostatistical research in the theory of exact tests, and on models for survival data and for ordinal data.
Applied Research in Social Sciences
The department also conducts applied research in collaboration with for example the Department of Social and Economic Geography, the Department of Sociology, the Department of Economic History, and the Division of Sociology of Law.
Stochastic Models and Computational Statistics
Spatial-temporal random fields with focus on alternatives to traditional linear models and Gaussian distributions. Extreme events analysis, stochastic geometry and dynamical extensions of the models. Applications for environmental sciences, engineering as well as for economic and biomedical data. Implementation of computationally intensive methods in non-standard settings: the Expectation and Maximization algorithm, statistical bootstrap and other resampling methods, Monte Carlo Markov Chains.
Noise Filtering Problem for Autogressive Functional Time Series
This research studies the functional autoregressive (FAR) model, which is distorted by a functional noise. Existing approaches to estimating the FAR model typically use functional principle components of covariance operators. However, we are aiming to get a better estimation of the autoregressive operator by using the regularization techniques. Additional to this fundamental FAR problem, we apply the current advances on the functional data filtering problem to find a method of filtering out additional functional noise that is distorting observation of the FAR model. There is significant practical relevance of the model since many observed time dependent functional data are marred by the observational noise. To examine utility of the proposed methods the large data set from the Human Connectome Project provided by Jaroslaw Harezlak, Indiana University will be analyzed.
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