Cemmap seminar presented by Victor Chernozhukov (MIT)

Abstract: We provide adaptive inference methods, based on l1 regularization methods, 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 from covariate distribution shifts and stochastic transformations, and average derivatives. Examples of non-regular functionals include the local linear functionals defined as local averages that approximate perfectly localized quantities: average treatment, average policy effects, and average derivatives, conditional on a covariate subvector fixed at a point. Our construction relies on building Neyman orthogonal equations for the target parameter that are approximately invariant to small perturbations of the nuisance parameters. To achieve this property we include the linear Riesz representer for the functionals in the equations as the additional nuisance parameter. We use l1-regularized methods to learn approximations to the regression function and the linear representer, in settings where dimension of (possibly overcomplete) dictionary of basis functions P is much larger than N. We then estimate the linear functional by the solution to the empirical analog of the orthogonal equations. Our key result is that under weak assumptions the estimator of the functional concentrates in a L/root(n) neighborhood of the target with deviations controlled by the Gaussian law, provided L/root(n) \to 0; L is the operator norm of the functional, measuring the degree of its non-regularity, with L diverging for local functionals (or under weak identification of the global functionals).

Papers can be found

here.

here.

here.

here.