A0747
Title: Temporal spatial model via trend filtering
Authors: Carlos Misael Madrid Padilla - University of Notre Dame (United States) [presenting]
Oscar Hernan Madrid - University of California Los Angeles (United States)
Daren Wang - Carnegie Mellon University (United States)
Abstract: The focus is on the estimation of a nonparametric regression function in the presence of data with temporal-spatial dependencies. In such a context, trend filtering, a nonparametric estimator, is studied. To the best of knowledge, this estimator has not previously been examined in a similar context. For univariate settings, the signals considered are assumed to have a kth weak derivative with bounded total variation, allowing for a general degree of smoothness. In the multivariate setting, we study a variant of the $K$-nearest neighbor fused lasso estimator. For this case, the function is required to have bounded variation and satisfy a property that extends a piecewise Lipschitz continuity criterion, or the function is assumed to be piecewise Lipschitz. An ADMM algorithm is developed for practical computation. By aligning with lower bounds, the minimax optimality of the univariate and multivariate estimators is shown. A unique phase transition phenomenon, previously unprecedented in trend filtering studies, emerges through the analysis. Both simulation studies and real data applications underscore the superior performance of the method when compared with established techniques in the existing literature.
