Tuning Parameter Selection for the Fused Lasso Signal Approximator

Abstract

In this thesis, we propose a two-stage tuning parameter selection procedure for the fused lasso signal approximator (FLSA). The FLSA can be used to recover piecewise constant mean vectors by penalizing the differences of the neighboring mean values. Like other regularized methods, choice of the tuning parameters affects the quality of model selection and estimation. We find a theoretically optimal fusion parameter for identifying the true changepoints. As a practical fusion parameter selection procedure, we propose a generalized information criteria (GIC) with theoretical justification. For any preliminary test statistic which has a piecewise constant mean structure, the adaptive fusion estimator built on the preliminary test statistic gives lower false discovery rate (FDR).