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Non-convex penalized estimation for the AR process
Commun. Stat. Appl. Methods, CSAM 2018;25:453-470
Published online September 30, 2018
© 2018 Korean Statistical Society.

Okyoung Naa, Sunghoon Kwon1,b

aDepartment of Applied Statistics, Kyonggi University, Korea;
bDepartment of Applied Statistics, Konkuk University, Korea
Correspondence to: Department of Applied Statistics, Konkuk University, 120 Neungdong-ro, Gwangjin-gu, Seoul 05029, Korea. E-mail: shkwon0522@konkuk.ac.kr
Received January 22, 2018; Revised April 3, 2018; Accepted April 4, 2018.
We study how to distinguish the parameters of the sparse autoregressive (AR) process from zero using a non-convex penalized estimation. A class of non-convex penalties are considered that include the smoothly clipped absolute deviation and minimax concave penalties as special examples. We prove that the penalized estimators achieve some standard theoretical properties such as weak and strong oracle properties which have been proved in sparse linear regression framework. The results hold when the maximal order of the AR process increases to infinity and the minimal size of true non-zero parameters decreases toward zero as the sample size increases. Further, we construct a practical method to select tuning parameters using generalized information criterion, of which the minimizer asymptotically recovers the best theoretical non-penalized estimator of the sparse AR process. Simulation studies are given to confirm the theoretical results.
Keywords : autoregressive process, subset selection, non-convex penalty, oracle property, tuning parameter selection