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Targeted undersmoothing


Hansen, Christian; Kozbur, Damian; Misra, Sanjog (2017). Targeted undersmoothing. arXiv 1706.07328, University of Zurich.

Abstract

This paper proposes a post-model selection inference procedure, called targeted undersmoothing, designed to construct uniformly valid confidence sets for a broad class of functionals of sparse high-dimensional statistical models. These include dense functionals, which may potentially depend on all elements of an unknown high-dimensional parameter. The proposed confidence sets are based on an initially selected model and two additionally selected models, an upper model and a lower model, which enlarge the initially selected model. We illustrate application of the procedure in two empirical examples. The first example considers estimation of heterogeneous treatment effects using data from the Job Training Partnership Act of 1982, and the second example looks at estimating profitability from a mailing strategy based on estimated heterogeneous treatment effects in a direct mail marketing campaign. We also provide evidence on the finite sample performance of the proposed targeted undersmoothing procedure through a series of simulation experiments.

Abstract

This paper proposes a post-model selection inference procedure, called targeted undersmoothing, designed to construct uniformly valid confidence sets for a broad class of functionals of sparse high-dimensional statistical models. These include dense functionals, which may potentially depend on all elements of an unknown high-dimensional parameter. The proposed confidence sets are based on an initially selected model and two additionally selected models, an upper model and a lower model, which enlarge the initially selected model. We illustrate application of the procedure in two empirical examples. The first example considers estimation of heterogeneous treatment effects using data from the Job Training Partnership Act of 1982, and the second example looks at estimating profitability from a mailing strategy based on estimated heterogeneous treatment effects in a direct mail marketing campaign. We also provide evidence on the finite sample performance of the proposed targeted undersmoothing procedure through a series of simulation experiments.

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Additional indexing

Item Type:Working Paper
Communities & Collections:03 Faculty of Economics > Department of Economics
Dewey Decimal Classification:330 Economics
Uncontrolled Keywords:Model selection, sparsity, dense functionals, hypothesis testing
Language:English
Date:June 2017
Deposited On:09 Feb 2018 10:35
Last Modified:20 Sep 2018 04:29
Series Name:arXiv
Number of Pages:42
ISSN:2331-8422
OA Status:Green
Free access at:Official URL. An embargo period may apply.
Official URL:https://arxiv.org/abs/1706.07328

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