Multi-SNP mediation intersection-union test

Intersection and Union Logic

Introduction to Intersection-union Tests

The Intersection-Union Test (IUT ) has become increasingly popular, especially through its application in bioequivalence testing. Here we will provide a basic introduction and discuss some properties of the IUT . Since this method is based upon a combination of tests, there may be a concern for the need of a multiplicity adjustment to adequately control the overall type-I error rate. We will ad...

Union-Intersection Multiple Comparison Tests

The union-intersection principle yields a class of multiple comparison tests that include the classical Scheffé tests for analysis of variance, and are easily applied to any likelihood ratio test. Examples are given.

Set systems with union and intersection constraints

Let 2 ≤ d ≤ k be fixed and n be sufficiently large. Suppose that G is a collection of k-element subsets of an n-element set, and |G| > ( n−1 k−1 ) . Then G contains d sets with union of size at most 2k and empty intersection. This verifies a conjecture of the first author for large n.

Worst Case Optimal Union-Intersection Expression Evaluation

We consider the problem of evaluating an expression consisting of unions and intersections of some sorted sets in the comparison model. Given the expression and the sizes of the sets, we are interested in the worst-case complexity of evaluating the expression in terms of the sizes of the sets. We assume the sets in the given expression are independent. We show a lower bound on this problem and ...