A0555
Title: Continuous-time multivariate analysis: The transpose of functional data analysis
Authors: Philip Reiss - University of Haifa (Israel) [presenting]
Biplab Paul - University of Haifa (Israel)
Erjia Cui - Johns Hopkins University (United States)
Abstract: The starting point for much multivariate analysis (MVA) is an $n\times p$ data matrix whose $n$ rows represent observations and whose $p$ columns represent variables. But some multivariate data sets may be best conceptualized not as $n$ discrete $p$-variate observations but as $p$ curves or functions defined on a common time interval. This viewpoint may be useful for data observed at very high time resolution, with unequal time intervals, and/or with substantial missingness. A framework for extending techniques of MVA is introduced to such settings by representing the curves as linear combinations of basis functions such as B-splines. This is formally identical to the Ramsay-Silverman representation of functional data. Still, whereas functional data analysis extends MVA to the case of observations that are curves rather than vectors heuristically, $n\times p$ data with $p$ infinite is instead concerned with what happens when $n$ is infinite. A simulation study demonstrates that the proposed continuous-time approach can improve the estimation of correlations among time series. A new R package, "ctmva", that translates the classical MVA methods of principal component analysis, Fisher's linear discriminant analysis, and $k$-means clustering is demonstrated in the above continuous-time setting. The methods are illustrated with a novel perspective on the well-known Canadian weather data set and with applications to neurobiological and environmental metric data.
