AVVISO DI SEMINARIO
Dipartimento di Matematica
Università di Roma Tor Vergata
Giovedì 14 Giugno Ore 12
Aula Dal Passo
Speaker: Victor Panaretos (EPFL)
DOUBLY SPECTRAL ANALYSIS OF FUNCTIONAL TIME SERIES AND DNA MOLECULAR DYNAMICS
The Karhunen-Loève (KL) expansion has evolved into the workhorse of functional data analysis: the Fourier representation it affords on the one hand serves as a basis for motivating methodology by analogy to multivariate statistics; and, on the other hand, appears as the natural means of regularization in problems such as regression, testing and prediction, which are ill-posed in the functional case. With the aim of obtaining a similarly canonical representation of dependent functional data, we develop a doubly spectral analysis of a stationary functional stochastic process, decomposing it into an integral of uncorrelated functional frequency components (Cramér representation), each of which is in turn expanded into a KL series. This Cramér-Karhunen-Loève representation separates temporal from intrinsic curve variation, and it is seen to yield a harmonic principal component analysis when truncated: a finite dimensional proxy of the time series that optimally captures both within and between curve variation. Empirical versions are introduced, and a rigorous analysis of their large-sample behaviour is provided under Brillinger mixing conditions. Our work is motivated by and applied to the study of the molecular dynamics of short strands of DNA; specifically, we consider the problem of determining whether the dynamics of such strands in solution are significantly affected by small perturbations of their base-pair composition, based on molecular dynamics simulations. (Based on joint work with Shahin Tavakoli, now at Warwick).