Abstract
Based on two independent samples drawn from univariate distributions with unknown densities f and g, I am interested in identifying subintervals where the two densities deviate significantly from each other. I will start motivating this problem with an example from gene therapy: here, two viruses are compared in their integration patterns into the genome. But there are several other situations which call for a local comparison of two densities. We turn the density comparison problem into a regression comparison problem, where several nonparametric regression procedures for detection of sparse signals can be performed. The methods we propose involve multiple testing, model selection and wavelets. I will present the theory, a simulation study and some results from gene therapy.
This is joint work with Hayat Mohammed and Anestis Antoniadis. The gene therapy study is joint work with A. Ambrosi, D. Pellin, C. Cattoglio, .F. Mavilio, C. Di Serio and A. Frigessi.