Correction: Approximate $p$-values for local sequence alignments
David Siegmund, Benjamin Yakir · The Annals of Statistics · 2003
Introduction.It has been pointed out to us by D. Metzler (University of Frankfurt) that the proof of Theorem 3 of Siegmund and Yakir ( 2000) is incomplete.In addition, S. Grossman (Frankfurt) and A. Dembo (Stanford) have observed that some conditions are required in order for the proofs of Theorems 1 and 2 (in particular the proof of Lemma 1) to hold.In this note we give appropriate additional conditions and complete the proof of Theorem 3. We use the notation of our earlier paper.To describe the conditions for Theorems 1 and 2, we let Q 0 denote the "null" probability given by Q) denote the implied "alternative."Also let Q i,j be defined to be the product probability that gives x the marginal distribution it has under Q i and y the marginal distribution it has under Q j .We assume that