This thesis considers identification, estimation, and inference in nonparametric settings. Special attention is given to identification with instrumental variables of small support, and in time series via the ergodic assumption. Chapter 1 considers a nonparametric instrumental regression model in which the regressor and instrument are discretely distributed. Here, we strengthen...
This dissertation proposes an oracle efficient estimator in the context of a sparse linear model. Chapter 1 introduces the penalty and the estimator that optimizes a penalized least squares objective. Unlike existing methods, the penalty is differentiable – once, and hence the estimator does not engage in model selection. This...