In this paper we analyze the asymptotic properties of l1 penalized maximum
likelihood estimation of signals with piece-wise constant mean values and/or
variances. The focus is on segmentation of a non-stationary time series with
respect to changes in these model parameters. This change point detection and
estimation problem is also referred to as total variation denoising or l1 -mean
filtering and has many important applications in most fields of science and
engineering. We establish the (approximate) sparse consistency properties,
including rate of convergence, of the so-called fused lasso signal approximator
(FLSA). We show that this only holds if the sign of the corresponding
consecutive changes are all different, and that this estimator is otherwise
incapable of correctly detecting the underlying sparsity pattern. The key idea
is to notice that the optimality conditions for this problem can be analyzed
using techniques related to brownian bridge theory.

本文分析了含分段常数均值和 / 或方差信号的 l1 惩罚最大似然估计的渐近性质，并建立了融合拉索信号逼近器的（近似的）稀疏一致性性质，重点研究了非平稳时间序列相对于这些模型参数的分段。