|M.Sc Student||Leibovici Yotam|
|Subject||Improving Efficiency of Tests for Composite Null Hypotheses|
|Department||Department of Industrial Engineering and Management||Supervisor||ASSOCIATE PROF. Yair Goldberg|
Mediation analysis, a research area within the field of causal inference, is a collection
of methods employed for studying the effect of an exposure on an outcome, interceded
by a mediator. In mediation analysis, two simple hypotheses are tested: the effect
of the exposure on the mediator, and the effect of the mediator on the outcome. In
standard tests for the composite hypothesis, the significance level can vary across scenarios
of the null. Under the scenario of either of the simple null hypotheses is true,
a predetermined significance level can be assured, while when both nulls are true, the
significance level tends to decrease significantly, turning the test into much more conservative.
Adaptively finding the correct scenario will enable us to customize our tests,
and consequently enlarge their efficiency. One way of doing so is to use two-stage
testing procedures. In this work we link between two-stage procedures and shrinkage
estimators, study the properties of shrinkage estimators, and characterize their behavior
in different parameter points using local asymptotics. We formulate theoretical
results about shrinkage estimators, compared to regular estimators, in different scenarios
of convergence rates and filtration probabilities, under some regularity conditions.
We then discuss the multiple-testing framework and state results about the two-stage
procedures and controlling the FWER. Taking advantage of these theoretical results,
we suggest a number of estimators and test statistics for the two-stage mediation procedures.
We then investigate their empirical FWER and power, compared to regular
estimators and tests, through simulations.