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The fused lasso is an important method for signal processing when the hiddensignals are sparse and blocky. It is often used in combination with the squaredloss function. However, the squared loss is not suitable for heavy tail errordistributions nor is robust against outliers which arise often in practice. Theleast absolute deviations (LAD) loss provides a robust alternative to thesquared loss. In this paper, we study the asymptotic properties of the fusedlasso estimator with the LAD loss for signal approximation. We refer to thisestimator as the LAD fused lasso signal approximator, or LAD-FLSA. Weinvestigate the estimation consistency properties of the LAD-FLSA and providesufficient conditions under which the LAD-FLSA is sign consistent. We alsoconstruct an unbiased estimator for the degrees of freedom of the LAD-FLSA forany given tuning parameters. Both simulation studies and real data analysis areconducted to illustrate the performance of the LAD-FLSA and the effect of theunbiased estimator of the degrees of freedom.

Estimation and Selection Properties of the LAD Fused Lasso Signal Approximator