Title: Stein's method applied to some statistical problems
Authors: Jay Bartroff - University of Southern California (United States) [presenting]
Abstract: Two instances of applying Stein's method to statistical problems are discussed. First, in the setting of group sequential testing methods where accumulating data is evaluated intermittently in stages, an existing multivariate Berry-Esseen bound based on Stein's method is applied to the joint distribution of MLEs of a vector parameter at each group analysis to obtain explicit bounds to its limiting normal distribution. The setting is a general parametric regression setup which allows the $i$-th observation to be the $i$-th subject's (say) response regressed on their covariates. Second, new and improved concentration inequalities are obtained via Stein's method for a class of multivariate occupancy models whose marginal distributions are lattice log concave and satisfy some other weak conditions. Examples with a statistical flavor in this class include degree counts in an Erdos-Renyi random graph, the number of neighbors and the volume covered by multi-way intersections in germ-grain models, bin occupancy counts in the multinomial model, and population sizes under multivariate hypergeometric sampling. In these models the new method provides concentration inequalities having the Poisson tail rate, many of which improve on those achieved by competing methods.