Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/246800 
Year of Publication: 
2021
Series/Report no.: 
cemmap working paper No. CWP32/21
Publisher: 
Centre for Microdata Methods and Practice (cemmap), London
Abstract: 
This paper is about the ability and means to root-n consistently and efficiently estimate linear, mean-square continuous functionals of a high dimensional, approximately sparse regression. Such objects include a wide variety of interesting parameters such as the covariance between two regression residuals, a coefficient of a partially linear model, an average derivative, and the average treatment effect. We give lower bounds on the convergence rate of estimators of such objects and find that these bounds are substantially larger than in a low dimensional, semiparametric setting. We also give automatic debiased machine learners that are 1/Í n consistent and asymptotically efficient under minimal conditions. These estimators use no cross-fitting or a special kind of cross-fitting to attain efficiency with faster than n−1/4 convergence of the regression. This rate condition is substantially weaker than the product of convergence rates of two functions being faster than 1/Í n, as required for many other debiased machine learners.
Subjects: 
Approximate sparsity
Lasso
debiased machine learning
linear functional
Riesz representer
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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