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Robertas Gabrys has research interest in functional data analysis and its applications in environmental sciences, financial econometrics, and space physics; statistical computing, and actuarial mathematics. His work has been published in the Journal of the Royal Statistical Society, Journal of Multivariate Analysis, Journal of the American Statistical Association, and Austrian Journal of Statistics.
RESEARCH + PUBLICATIONS
Reviewed 6 chapters for for Data Analytics, 1e by Alison Kelly, Sanjiv Jaggia, Kevin Lertwachara, Leida Chen 6 on the general content, organization, and approach of the text: Chapter 6: Regression AnalysisChapter 7: Advanced Regression AnalysisChapter 8: Introduction to Data MiningChapter 9: Supervised Data Mining: k-Nearest Neighbors and Naïve BayesChapter 10: Supervised Data Mining: Decision TreesChapter 11: Unsupervised Data Mining
A functional time series consists of curves, typically one curve per day. The most
important parameter of such a series is the mean curve. We propose two methods
of detecting a change in the mean function of a functional time series. The change
is detected on line, as new functional observations arrive. The general methodology
is motivated by and applied to the detection of a change in the average intraday
volatility pattern. The methodology is asymptotically justified by applying a new
notion of weak dependence for functional time series. It is calibrated and validated
by simulations based on real intraday volatility curves.
The paper proposes two inferential tests for error correlation in the functional linear model, which complement the available graphical
goodness-of-fit checks. To construct them, finite dimensional residuals are computed in two different ways, and then their autocorrelations
are suitably defined. From these autocorrelation matrices, two quadratic forms are constructed whose limiting distribution are chi-squared
with known numbers of degrees of freedom (different for the two forms). The asymptotic approximations are suitable for moderate sample
sizes. The test statistics can be relatively easily computed using the R package fda, or similar MATLAB software. Application of the tests
is illustrated on magnetometer and financial data. The asymptotic theory emphasizes the differences between the standard vector linear
regression and the functional linear regression. To understand the behavior of the residuals obtained from the functional linear model,
the interplay of three types of approximation errors must be considered, whose sources are: projection on a finite dimensional subspace,
estimation of the optimal subspace, and estimation of the regression kernel.