arXiv 14 Nov 2024 · Mathematics — Statistics Theory
arXiv:2411.09258 · PDF · DOI · OpenAlex · Extracted main text
Asymptotic optimality is a key theoretical property in model averaging. Due to technical difficulties, existing studies rely on restricted weight sets or the assumption that there is no true model with fixed dimensions in the candidate set. The focus of this paper is to overcome these difficulties. Surprisingly, we discover that when the penalty factor in the weight selection criterion diverges with a certain order and the true model dimension is fixed, asymptotic loss optimality does not hold, but asymptotic risk optimality does. This result differs from the corresponding result of Fang et al. (2023, Econometric Theory 39, 412-441) and reveals that using the discrete weight set of Hansen (2007, Econometrica 75, 1175-1189) can yield opposite asymptotic properties compared to using the usual weight set. Simulation studies illustrate the theoretical findings in a variety of settings.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Fang, F., Yuan, C., and Tian, W (2023) An asymptotic theory for least squares model averaging with nested models | 1.000 | 25 | 5 | 100% |
| 2 | Hansen, B. E (2007) Least squares model averaging | 1.000 | 8 | 4 | 100% |
| 3 | Zhang, X. and Liu, C.-A (2019) Inference after model averaging in linear regression models self | 1.000 | 7 | 4 | 100% |
| 4 | Peng, J., Li, Y., and Yang, Y (2024) On optimality of Mallows model averaging | 1.000 | 6 | 3 | 100% |
| 5 | Wan, A. T., Zhang, X., and Zou, G (2010) Least squares model averaging by Mallows criterion self | 1.000 | 5 | 3 | 100% |
| 6 | Zhang, X., Zou, G., Liang, H., and Carroll, R. J (2020) Parsimonious model averaging with a diverging number of parameters self | 0.974 | 13 | 5 | 92% |
| 7 | Zhang, X (2021) A new study on asymptotic optimality of least squares model averaging self | 0.928 | 4 | 3 | 100% |
| 8 | Hansen, B. E. and Racine, J. S (2012) Jackknife model averaging | 0.843 | 3 | 3 | 100% |
| 9 | Shao, J (1997) An asymptotic theory for linear model selection | 0.737 | 3 | 2 | 100% |
| 10 | Ding, J., Tarokh, V., and Yang, Y (2018) Model selection techniques: An overview | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 31 scored citations.