טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentLeibovici Yotam
SubjectImproving Efficiency of Tests for Composite Null Hypotheses
DepartmentDepartment of Industrial Engineering and Management
Supervisor ASSOCIATE PROF. Yair Goldberg


Abstract

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.