Minimax Semiparametric Learning With Approximate Sparsity

Jelena Bradic, Victor Chernozhukov, Whitney Newey and Yinchu Zhu ()

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Abstract: This paper is about the feasibility and means of root-n consistently estimating linear, mean-square continuous functionals of a high dimensional, approximately sparse regression. Such objects include a wide variety of interesting parameters such as regression coefficients, average derivatives, and the average treatment effect. We give lower bounds on the convergence rate of estimators of a regression slope and an average derivative and find that these bounds are substantially larger than in a low dimensional, semiparametric setting. We also give debiased machine learners that are root-n consistent under either a minimal approximate sparsity condition or rate double robustness. These estimators improve on existing estimators in being root-n consistent under more general conditions that previously known.

Date: 2019-12, Revised 2022-08
New Economics Papers: this item is included in nep-big
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1912.12213

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