基于LAD-LASSO方法的逐段常数序列中的变点估计

Estimation of Change Points in Piecewise Constant Time Series Based on LAD-LASSO Variable Selection Method

结构突变(变点)问题是统计学、经济学和信号处理等领域中的热点问题之一。当误差分布服从重尾分布或数据集含异常值时,LAD估计比OLS估计更加稳健;LASSO是一种流行的压缩估计和变量选择方法,将这两种经典的方法结合起来,提出基于LAD-LASSO的逐段常数时间序列变点估计的一种新的研究方法,其基本思想是把变点估计问题转化成变量选择问题来处理,在转化过程中对相应优化问题的约束条件仅做一次松弛。随机模拟表明:所提出的估计方法是切实可行的,算法更加简单易行,且估计结果具有很好的稳健性。

Structural break （change point） problem is one of the hot issues in statistics ,economics and signal processing fields and so on .Least absolute deviation （LAD） estimator is more robust than ordinary least squares （OLS） estimator ,especially when datasets subject to heavy -tailed errors or outliers .Least absolute shrinkage and selection operator （LASSO ） is a popular choice for shrinkage estimation and variable selection .In the paper ,we combine these two classical ideas together to put forward a novel method based on LAD‐LASSO to estimate change points in piecewise constant time series .The basic idea is converting the change point estimation problems into variable selection problems .In converting process we only make one relaxation to the constraint conditions of corresponding optimization problem . Simulation shows that the new method we proposed is really feasible ,algorithm is easier ,and estimators are robust .