We study trend filtering, a recently proposed tool of Kim et al. (2009) for nonparametric regression. The trend filtering estimate is defined as the minimizer of a penalized least squares criterion, in which the penalty term sums the absolute kth order discrete derivatives over the input points. Perhaps not surprisingly, trend filtering estimates appear to have the structure of kth degree splin...

Bayesian modeling method and slice analysis techniques show good effect in cycle-accurate power analysis of combinational circuit. In this paper, we use virtual signal logical depth assignment to resolve the problem that signal loop can not be sliced in sequential circuits. With this method, we build cycle-accurate power model based on Bayesian inference and slice analysis techniques. The exper...

Estimation of covariance function parameters of the error process in the presence of an unknown smooth trend is an important problem because solving it allows one to estimate the trend nonparametrically using a smoother corrected for dependence in the errors. Our work is motivated by spatial statistics but is applicable to other contexts where the dimension of the index set can exceed one. We o...

Recent work on trend-cycle decompositions for US real GDP yields the following puzzling features: methods based on Unobserved Components models, the BeveridgeNelson decomposition, the Hodrick-Prescott filter and others yield very different cycles which bear little resemblance to the NBER chronology, ascribes much movements to the trend leaving little to the cycle, and some imply a negative corr...

1 Trend and Cycle Decomposition y t = t + t where y t is an n 1 vector and t and t represent trend and cycle components respectively. This decomposition into components is not unique. Beveridge and Nelson (1981) and Stock and Watson (1988) derive the following decomposition: y t = C(L)" t = C(1)" t + (1 L)C (L)" t Integrating up gives: y t = C(1) 1 X i=0 " ti | {z } + C (L)" t | {z } trend cycl...