Consistencies and rates of convergence of jump-penalized least squares estimators
跳跃惩罚最小二乘估计的一致性与收敛速度
We study the asymptotics for jump-penalized least squares regression aiming at approximating a regression function by piecewise constant functions. Besides conventional consistency and convergence rates of the estimates in L2([0, 1)) our results cover other metrics like Skorokhod metric on the space of càdlàg functions and uniform metrics on C([0, 1]). We will show that these estimators are in an adaptive sense rate optimal over certain classes of “approximation spaces.”…