### Least Squares Model Averaging for Two Non-Nested Linear Models

GAO Yan1, XIE Tianfa2, ZOU Guohua3

1. 1. Department of Statistics, College of Science, Minzu University of China, Beijing 100081, China;
2. Faculty of Science, Beijing University of Technology, Beijing 100124, China;
3. School of Mathematical Sciences, Capital Normal University, Beijing 100048, China
• Received:2021-05-25 Revised:2021-08-11 Online:2023-01-25 Published:2023-02-09
• Supported by:
This research was supported by the National Natural Science Foundation of China under Grant Nos. 11801598, 12031016 and 11971323, the National Statistical Research Program under Grant No. 2018LY96, the Beijing Natural Science Foundation under Grant No. 1202001, and NQI Project under Grant No. 2022YFF0609903.

GAO Yan, XIE Tianfa, ZOU Guohua. Least Squares Model Averaging for Two Non-Nested Linear Models[J]. Journal of Systems Science and Complexity, 2023, 36(1): 412-432.

This paper studies the least squares model averaging methods for two non-nested linear models. It is proved that the Mallows model averaging weight of the true model is root-$n$ consistent. Then the authors develop a penalized Mallows criterion which ensures that the weight of the true model equals 1 with probability tending to 1 and thus the averaging estimator is asymptotically normal. If neither candidate model is true, the penalized Mallows averaging estimator is asymptotically optimal. Simulation results show the selection consistency of the penalized Mallows method and the superiority of the model averaging approach compared with the model selection estimation.
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