High-dimensional and causal inference are topics at the forefront of statistical research. This thesis is a unified treatment of three contributions to these literatures. The first two contributions are to the theoretical statistical literature; the third puts the techniques of causal inference into practice in policy evaluation.
In Chapter 2, we suggest a broadly applicable remedy for the failure of Efron’s bootstrap in high dimensions is to modify the bootstrap so that data vectors are broken into blocks and the blocks are resampled independently of one another. Cross-validation can be used effectively to choose the optimal block length. We show both theoretically and in numerical studies that this method restores consistency and has superior predictive performance when used in combination with Breiman’s bagging procedure. This chapter is joint work with Peter Hall and Hugh Miller.
In Chapter 3, we investigate regression adjustment for the modified outcome (RAMO). An equivalent procedure is given in Rubin and van der Laan [2007] and then in Luedtke and van der Laan [2016]; philosophically similar ideas appear to originate in Miller [1976]. We establish new guarantees when the procedure is applied in designed experiments (where the propensity score is known a priori) and confirm that the procedure is doubly robust. RAMO can be implemented in only a few lines of code and it can be immediately combined with existing regression models, including random forests and deep neural networks, used in classical prediction problems. This chapter is joint work with Bin Yu and Jasjeet Sekhon.
In Chapter 4, we investigate the specific deterrent effect of traffic citations. In Queensland, Australia many speeding and red-light running offenses are detected by traffic cameras and drivers are notified of the citation, not at the time they commit the offense, but when the citation notice is delivered by mail about two weeks later. We use a regression discontinuity design to assess whether the chance of crashing or recidivism changes at the moment of notification. We analyzed a population of nearly 3 million drivers who committed camera-detected offenses. We conclude that there is not a significant change in the incidence of crashes but there is a marked decrease in recidivism of about 25%. This chapter is joint work with David Studdert and Jeremy Goldhaber-Fiebert.
