Exercise4.17 In agenomicstudyresearcherswanttoidentifydifferentlyexpressedgeneswithin a setof m genes. Let Yj N (j,2) be theobservedexpressionlevelofthe j-th gene, j

Exercise4.17 ∗ In agenomicstudyresearcherswanttoidentifydifferentlyexpressedgeneswithin a setof m genes. Let Yj ∼N (μj,σ2) be theobservedexpressionlevelofthe j-th gene, j =1, ...,m.

Forsimplicityassumethat Yj’sareindependent(maybenotsorealisticinpractice)and σ2 is known.

Thus, weneedtotestsimultaneously H0 j : μj =0 (nondifferentiallyexpressedgene)vs. H1 j : μj ̸=0

(differentiallyexpressedgene).Evidently, H0 j will berejectedif |Yj| is large(GLRT).Applyvarious multiple testingprocedurestofindthecorrespondingthresholdsfor |Yj|’s:

1. What istheBonferroniFWERcontrollingprocedureatlevel α?

2. DerivetheHolmandHochbergprocedurestocontrolFWERatlevel α.

3. Which oftheaboveFWERcontrollingproceduresisthemostpowerful?

4. DerivetheBenjamini–HochbergFDRcontrollingprocedureatlevel α.

5. Forwhichoftheaboveprocedurestheindependenceassumptionisnecessary?