Abstract: Two topics in the area of dimension reduction for multiple populations will be explored. We will first propose a link-free test for testing whether two (or more) multi-index models share identical indices via the sufficient dimension reduction approach. Test statistics are developed based upon sufficient dimension reduction methods. The asymptotic null distributions of our test statistics are derived. Next, we will propose a two-step dimension reduction method for multi-population data. Our method is the first one in the area which could conduct a joint analysis while still retaining the population specific effects. Though partial dimension reduction (Chiaromonte et al., 2002) can be adopted to deal with multi-population dimension reduction, it encloses the related directions for all populations, population-specific effects are ignored. On the other side, unlike the conditional analysis which is carried out separately within each individual population, our method makes use of the information across the multiple populations which greatly improve the estimation accuracy. Simulations and a real data example were given to illustrate our methodology.
Host: Todd Kuffner