Post date: Apr 10, 2017 7:55:33 PM
SLAM & Causal Inference Working Groups Joint Short Course
"Empirical likelihood and some applications to biased sampling problems"
Peisong Han, Dept of Statistics and Actuarial Science, University of Waterloo
[abstract] The empirical likelihood (EL) methodology has been widely used and has led to remarkable successes in many research areas including statistics/biostatistics. This short course covers some basic theory and implementation of EL and some applications in missing-data analysis and causal inference.
Part I will cover EL and one of its main alternatives, exponential tilting (ET), within the “generalized empirical likelihood” (Newey and Smith 2004) framework. We will consider the typical setting of semiparametric models defined by estimating equations. Both EL and ET can be viewed as either a “minimum discrepancy” estimator or a “saddle-point” estimator. We will also cover the implementation based on the “saddle-point” representation through a nested optimization. A Newton-Raphson-type algorithm will be introduced and some relevant issues will be discussed.
Part II will focus on some applications in missing-data analysis and causal inference. Many such EL-based methods can be unified within the “generalized pseudo-EL” (Tan and Wu 2015) framework. Such methods have desirable properties on both the robustness and the efficiency of estimation. Robustness-wise, some estimators are consistent if any one of the multiple working models for the propensity score and for the data distribution is correctly specified. Efficiency-wise, in addition to being locally efficient, some estimators achieve “intrinsic efficiency” so that, when the propensity score is correctly modeled, even the incorrect data distribution models can be used to improve efficiency. Applied to causal inference, such methods explicitly achieve covariate balancing between the treatment and control groups.