2016/06/21 by Kevin Lin, James Sharpnack, Lin, Kevin +5 · 2 citations
Mathematics · Economics, Econometrics and Finance · #Statistical Methods and Inference #Advanced Causal Inference Techniques #Health Systems, Economic Evaluations, Quality of Life
paper · pdf · doi:10.48550/arxiv.1606.06746
In the 1-dimensional multiple changepoint detection problem, we prove that any procedure with a fast enough ℓ2 error rate, in terms of its estimation of the underlying piecewise constant mean vector, automatically has an (approximate) changepoint screening property---specifically, each true jump in the underlying mean vector has an estimated jump nearby. We also show, again assuming only knowledge of the ℓ2 error rate, that a simple post-processing step can be used to eliminate spurious estimated changepoints, and thus delivers an (approximate) changepoint recovery property---specifically, in addition to the screening property described above, we are assured that each estimated jump has a true jump nearby. As a special case, we focus on the application of these results to the 1-dimensional fused lasso, i.e., 1-dimensional total variation denoising, and compare the implications with existing results from the literature. We also study extensions to related problems, such as changepoint detection over graphs.