arXiv 5 May 2024 · Econometrics · 18 citations (OpenAlex)
arXiv:2405.03021 · PDF · DOI · OpenAlex · Extracted main text
I review some of the main methods for selecting tuning parameters in nonparametric and $\ell_1$-penalized estimation. For the nonparametric estimation, I consider the methods of Mallows, Stein, Lepski, cross-validation, penalization, and aggregation in the context of series estimation. For the $\ell_1$-penalized estimation, I consider the methods based on the theory of self-normalized moderate deviations, bootstrap, Stein's unbiased risk estimation, and cross-validation in the context of Lasso estimation. I explain the intuition behind each of the methods and discuss their comparative advantages. I also give some extensions.
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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 | Lecue and Mitchell (2012) Oracle inequalities for cross-validation type procedures | 0.737 | 3 | 2 | 100% |
| 2 | Belloni, Chen, Chernozhukov and Hansen (2012) Sparse models and methods for optimal instruments with an application to eminent domain | 0.693 | 7 | 1 | 100% |
| 3 | Zou, Hastie and Tibshirani (2007) On the degrees of freedom of the lasso | 0.693 | 5 | 1 | 100% |
| 4 | Chetverikov and Sorensen (2021) Analytic and bootstrap-after-cross-validation methods for selecting penalty parameters of high-dimensional m-estimators | 0.644 | 4 | 1 | 100% |
| 5 | Tibshirani and Taylor (2012) Degrees of freedom in lasso problems | 0.644 | 4 | 1 | 100% |
| 6 | Arlot and Celisse (2010) A survey of cross-validation procedures for model selection | 0.644 | 2 | 2 | 100% |
| 7 | Bischl et al (2023) Hyperparameter optimization: Foundations, algorithms, best practices, and open challenges | 0.644 | 2 | 2 | 100% |
| 8 | Chernozhukov, Chetverikov and Kengo (2013) Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors | 0.644 | 2 | 2 | 100% |
| 9 | Chernozhukov, Chetverikov and Kengo (2017) Central limit theorems and bootstrap in high dimensions | 0.644 | 2 | 2 | 100% |
| 10 | Chernozhukov, Chetverikov, Kengo and Koike (2022) Improved central limit theorem and bootstrap approximations in high dimensions | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 63 scored citations.
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| Citing paper | Intensity | Mentions | Sections | |
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| 1 | Reproducible Aggregation of Sample-Split Statistics$^*$ | 0.405 | 1 | 1 |