We formulate a general cross validation framework for signal denoising. The general framework is then applied to nonparametric regression methods such as Trend Filtering and Dyadic CART. The resulting cross validated versions are then shown to attain nearly the same rates of convergence as are known for the optimally tuned analogues. There did not exist any previous theoretical analyses of cross validated versions of Trend Filtering or Dyadic CART. Our general framework is inspired by the ideas in Chatterjee and Jafarov (2015) and is potentially applicable to a wide range of estimation methods which use tuning parameters. BIO: Sabyasachi Chatterjee is an Assistant Professor (from 2017 onwards) in the Statistics Department at University of Illinois at Urbana Champaign. Most of his research has been in Statistical Signal Processing. His is also interested in Probability and all theoretical aspects of Machine Learning. He obtained his Phd in 2014 at Yale University and then was a Kruskal Instructor at University of Chicago till 2017.
