Efficient Estimation of Quantiles in Missing Data Models
Venue
Google Inc., 111 8th Avenue (2015)
Publication Year
2015
Authors
Ivan Diaz
BibTeX
Abstract
We present a method to estimate the quantile of a variable subject to missingness,
under the missing at random assumption. Our proposed estimator is locally
efficient, root-n-consistent, asymptotically normal, and doubly robust, under
regularity conditions. We use Monte Carlo simulation to compare our proposal to the
one-step and inverse-probability weighted estimators. Our estimator is superior to
both competitors, with a mean squared error up to 8 times smaller than the one-step
estimator, and up to 2.5 times smaller than an inverse probability weighted
estimator. We develop extensions for estimating the causal effect of treatment on a
population quantile among the treated. Our methods are motivated by an application
with a heavy tailed continuous outcome. In this situation, the efficiency bound for
estimating the effect on the mean is often large or infinite, ruling out
root-n-consistent inference and reducing the power for testing hypothesis of no
treatment effect. Using quantiles (e.g., the median) may yield more accurate
measures of the treatment effect, along with more powerful hypothesis tests. In our
application, the proposed estimator of the effect on the median yields hypothesis
tests of no treatment effect up to two times more powerful, and its variance is up
to four times smaller than the variance of its mean counterpart.
