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Title: smoothEM: A new approach for the simultaneous assessment of smooth curves and spikes Authors:  Marzia Cremona - Université Laval (Canada) [presenting]
Huy Dang - Penn State University (United States)
Francesca Chiaromonte - The Pennsylvania State University (United States)
Abstract: Many longitudinal data comprise both smooth and irregular elements. We consider scenarios in which an underlying smooth curve is composed not just of Gaussian errors, but also of irregular spikes that (a) are themselves of interest, and (b) can negatively affect our ability to characterize the underlying curve. We propose an approach that, combining regularized spline smoothing and an EM algorithm, allows us to both identify spikes and estimate the smooth component. We prove the convergence of EM estimates to the true population parameters under some assumptions. Next, we demonstrate the performance of our method on finite samples and its robustness to assumptions' violations through simulations. Finally, we apply it to the analysis of two time series on the annual heatwaves index in the US and on the weekly electricity consumption in Ireland. In both datasets, we are able to characterize underlying smooth trends and pinpoint irregular/extreme behaviors.