Super Learner Based Conditional Density Estimation with Application to Marginal Structural Models

Ivan Diaz, University of California, Berkeley, School of Public Health - Division of Biostatistics
Mark J. van der Laan, University of California, Berkeley; School of Public Health - Division of Biostatistics

Abstract

In this paper we present a histogram-like estimator of a conditional density that uses super learner crossvalidation to estimate the histogram probabilities, as well as the optimal number and position of the bins. This estimator is an alternative to kernel density estimators when the dimension of the problem is large. We demonstrate its applicability to estimation of Marginal Structural Model (MSM) parameters in which an initial estimator of the treatment %mechanism is needed. MSM estimation based on the proposed density estimator results in less biased estimates, when compared to estimates based on a misspecified parametric model.