Rank tests for interaction in two-way layouts with application in genetic analysis

Abstract

To fully dissect complex traits, it is desirable to have methods able to test gene-gene interaction for human genetic data. This thesis provides a framework to process human quantitative trait data such that the problem becomes a hypothesis test of interaction for a two-way layout design with unequal replicates. Three new nonparametric rank tests are proposed. Their limiting distributions under Pitman alternatives and asymptotic relative efficiencies are studied. The tests are extended to unbalanced designs. We also introduce the notion of composite linear rank statistics and prove asymptotic normality under mild conditions. Consistent estimators are provided for the limiting variance-covariance matrix of arbitrary linear rank statistics.