arXiv 16 Oct 2025 · Mathematics — Statistics Theory
arXiv:2510.14822 · PDF · Extracted main text
Model selection criteria are one of the most important tools in statistics. Proofs showing a model selection criterion is asymptotically optimal are tailored to the type of model (linear regression, quantile regression, penalized regression, etc.), the estimation method (linear smoothers, maximum likelihood, generalized method of moments, etc.), the type of data (i.i.d., dependent, high dimensional, etc.), and the type of model selection criterion. Moreover, assumptions are often restrictive and unrealistic making it a slow and winding process for researchers to determine if a model selection criterion is selecting an optimal model. This paper provides general proofs showing asymptotic optimality for a wide range of model selection criteria under general conditions. This paper not only asymptotically justifies model selection criteria for most situations, but it also unifies and extends a range of previously disparate results.
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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 | Shao, J (1997) An asymptotic theory for linear model selection | 1.000 | 5 | 3 | 100% |
| 2 | Li, K.-C (1987) Asymptotic optimality for cp, cl, cross-validation,and generalized cross-validation: Discrete index set | 0.811 | 4 | 2 | 100% |
| 3 | Hansen, B. E. and J. Racine (2012) Jackknife model averaging | 0.737 | 3 | 2 | 100% |
| 4 | Sin, C.-Y. and H. White (1996) Information criteria for selecting possibly misspecified parametric models | 0.644 | 4 | 1 | 100% |
| 5 | Burman, P., E. Chow, and D. Nolan (1994) A cross-validatory method for dependent data | 0.644 | 2 | 2 | 100% |
| 6 | Claeskens, G (2016) Statistical model choice | 0.644 | 2 | 2 | 100% |
| 7 | Clark, T. E. and M. W. McCracken (2009) Improving forecast accuracy by combining recursive and rolling forecasts | 0.644 | 2 | 2 | 100% |
| 8 | Ding, J., V. Tarokh, and Y. Yang (2018) Model selection techniques–-an overview | 0.644 | 2 | 2 | 100% |
| 9 | Lütkepohl, H (2005) New Introduction to Multiple Time Series Analysis | 0.644 | 2 | 2 | 100% |
| 10 | Rossi, B (2021) Forecasting in the presence of instabilities: How we know whether models predict well and how to improve them | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 65 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | A Note on the Finite Sample Bias in Time Series Cross-Validation | 0.405 | 1 | 1 |