My current research is based in an area of statistics called functional data analysis (FDA). This area of statistics focuses on the analysis and theory of data that are in the form of functions, surfaces, images, shapes, or more general objects varying over a continuum. In the era of BIG DATA, FDA provides novel approaches to complex analytics problems.
Although my research interest in FDA spans a wider range of topics, my current work in this field can be categorized into two main topics: (1) change point analysis and (2) machine learning methods for functional/high dimensional time series forecasting
- Functional data analysis
- Structural breaks analysis for dependent data
- Machine learning methods for time series forecasting
- Statistical computing
R Package fChange: Change Point Analysis in Functional Data
Change point estimation and detection methods for functional data are implemented using dimension reduction via functional principal component analysis and a fully-functional (norm-based) method. Detecting and dating structural breaks for both dependent and independent functional samples is illustrated along with some basic functional data generating processes.
APPLIED TIME SERIes
- Decomposition of time series into trend, seasonality and dependent errors
- Modeling of dependent errors: stationarity, linear time series, ARMA processes
- Estimation and prediction of stationary time series
- Spectral analysis: cyclical behavior, periodicity and periodogram
- Asymptotic theory (LLN, CLT, Convergence in prob., distr., etc,...)
- Hypothesis testing (UMP tests, two sided tests, t-test, f-test, bayes test)
- Categorical and non parametric methods
- Linear statistical models
I taught the time series class during F2017, W2017, F2016, W2016, F2015, and the mathematical statistics class during S2015, S2016, S2017. besides these two main classes I also taught "Statistics for biological sciences", and also "Univariate and Multivariate Calculus".