Local regression distribution estimators

This paper investigates the large sample properties of local regression distribution estimators, which include a class boundary adaptive density estimators as prime example. First, we establish pointwise Gaussian distributional approximation in unified way, allowing for both and interior evaluation points simultaneously. Using this result, study asymptotic efficiency show that carefully crafted minimum distance implementation based on “redundant” regressors can lead to gains. Second, uniform linearizations strong approximations employ these results construct valid confidence bands. Third, develop extensions weighted distributions with estimated weights L2 estimation. Finally, illustrate our methods two applications program evaluation: counterfactual testing, IV specification heterogeneity analysis. Companion software packages Stata R are available.