We provide novel adaptive inference methods, based on \ell_1 regularization, for regular ( semi-parametric ) and non-regular (nonparametric) linear functionals of the conditional expectation function. Examples of regular functionals include average treatment effects, policy effects, and derivatives. Examples of non-regular functionals include localized quantities: average treatment effects, policy effects, and derivatives conditional on a covariate subvector fixed at a point. We construct a Neyman orthogonal equation for the target parameter that is approximately invariant to small perturbations of the nuisance parameters. To achieve this property, we include the linear Riesz representer for the functional as an additional nuisance parameter. Under weak assumptions, the estimator of the functional concentrates in a L/\sqrt{n Our analysis yields weak `` double sparsity robustness '' : either the approximation to the regression or the approximation to the representer can be ``completely dense'' as long as the other is sufficiently ``sparse'' . Our main results are non-asymptotic and imply asymptotic uniform validity over large classes of models, translating into honest confidence bands for both global and local parameters.
We provide adaptive inference methods, based on \ell_1 regularization, for regular ( semiparametric ) and non-regular (nonparametric) linear functionals of the conditional expectation function. Examples of regular functionals include average treatment effects, policy effects, and derivatives. Examples of non-regular functionals include average treatment effects, policy effects, and derivatives conditional on a covariate subvector fixed at a point. We construct a Neyman orthogonal equation for the target parameter that is approximately invariant to small perturbations of the nuisance parameters. To achieve this property, we include the Riesz representer for the functional as an additional nuisance parameter. Our analysis yields weak " double sparsity robustness " : either the approximation to the regression or the approximation to the representer can be "completely dense" as long as the other is sufficiently "sparse" . Our main results are non-asymptotic and imply asymptotic uniform validity over large classes of models, translating into honest confidence bands for both global and local parameters.
D
novel
R
semi-parametric
semiparametric
D
localized quantities:
D
linear
D
Under weak assumptions, the estimator of the functional concentrates in a L/\sqrt{n
R
``
"
R
''
"
R
``completely dense''
"completely dense"
R
``sparse''
"sparse"