Eric Mbakop, Max Tabord-Meehan
arXiv 11 Sep 2016 · Mathematics — Statistics Theory
arXiv:1609.03167 · PDF · Extracted main text
This paper studies a penalized statistical decision rule for the treatment assignment problem. Consider the setting of a utilitarian policy maker who must use sample data to allocate a binary treatment to members of a population, based on their observable characteristics. We model this problem as a statistical decision problem where the policy maker must choose a subset of the covariate space to assign to treatment, out of a class of potential subsets. We focus on settings in which the policy maker may want to select amongst a collection of constrained subset classes: examples include choosing the number of covariates over which to perform best-subset selection, and model selection when approximating a complicated class via a sieve. We adapt and extend results from statistical learning to develop the Penalized Welfare Maximization (PWM) rule. We establish an oracle inequality for the regret of the PWM rule which shows that it is able to perform model selection over the collection of available classes. We then use this oracle inequality to derive relevant bounds on maximum regret for PWM. An important consequence of our results is that we are able to formalize model-selection using a "hold-out" procedure, where the policy maker would first estimate various policies using half of the data, and then select the policy which performs the best when evaluated on the other half of the data.
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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 | Bartlett, Peter L, Stéphane Boucheron, and Gábor Lugosi (2002) Model selection and error estimation | 0.928 | 5 | 3 | 80% |
| 2 | Kitagawa, Toru and Aleksey Tetenov (2018) Who should be treated? empirical welfare maximization methods for treatment choice | 0.902 | 30 | 6 | 73% |
| 3 | Györfi, L, L Devroye, and G Lugosi (1996) A probabilistic theory of pattern recognition | 0.874 | 6 | 3 | 67% |
| 4 | Athey, Susan and Stefan Wager (2017) Efficient policy learning | 0.874 | 5 | 2 | 100% |
| 5 | Koltchinskii, Vladimir (2001) Rademacher penalties and structural risk minimization | 0.737 | 3 | 2 | 100% |
| 6 | Boucheron, Stéphane, Olivier Bousquet, and Gábor Lugosi (2005) Theory of classification: A survey of some recent advances | 0.644 | 2 | 2 | 100% |
| 7 | Kallus, Nathan (2016) Learning to personalize from observational data | 0.644 | 2 | 2 | 100% |
| 8 | Koltchinskii, V (2008) Oracle inequalities in empirical risk minimization and sparse recovery problems: Lecture notes. Technical report, Technical repo… | 0.644 | 2 | 2 | 100% |
| 9 | Manski, Charles F (2004) Statistical treatment rules for heterogeneous populations | 0.644 | 2 | 2 | 100% |
| 10 | Stoye, Jörg (2009) Minimax regret treatment choice with finite samples | 0.644 | 2 | 2 | 100% |
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arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.