A note on the monotonicity of the ES-algorithm

• Main Author: WU, Zhengxiao
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2011
• Subjects: ES algorithm; M-estimation; penalized least-squares; pseudo-data; robust smoothing; Theory and Algorithms
• Online Access: https://ink.library.smu.edu.sg/soe_research_all/13
• Institution: Singapore Management University

In the study of the robust nonparametric regression problem, Oh et al. [The role of pseudo data for robust smoothing with application to wavelet regression, Biometrika 94 (2007), pp. 893–904] developed and named the ES algorithm. In the event that the ES algorithm converges, the robust estimator can be obtained through a sequence of conventional penalized least-squares estimates, the computation of which is fast and straightforward. However, the convergence of the ES algorithm was not established theoretically in Oh et al. In this note, we show that under a certain simple condition, the ES algorithm is monotonic. In particular, the ES algorithm does converge globally in the setting of Oh et al.