Tuning parameter selection in fused lasso signal approximator with false discovery rate control

Abstract

The fused lasso signal approximator (FLSA) obtains sparse and blocky estimates of the piecewise constant mean model with two tuning parameters for the total variation (TV)-norm and ${\ell }_1$-norm penalties. The FLSA can be divided into the fusion procedure for finding block structures and the soft-thresholding procedure for identifying non-zero block signals. In this paper, we first prove that Bayesian information criterion-type criteria guarantee that the FLSA obtains the minimally over-fitted block estimates. Second, we propose a new procedure to select the soft-thresholding level that controls the false discovery rate of the estimated signals for identifying non-zero signals under the aimed level based on the preliminary test statistics. We show that the soft-thresholded fusion estimators improve the preliminary test statistics regarding false discovery rates. We apply the FLSA with the proposed selection procedure to the COVID-19 pandemic dataset in Korea to identify the change points.