Title: On estimation and prediction for high-dimensional Poisson models with quasi zero inflation
Authors: Keisuke Yano - The University of Tokyo (Japan) [presenting]
Abstract: The problem of estimating and predicting high-dimensional Poisson models with quasi zero inflation is discussed. In analyzing count data, exact or quasi zero inflation often appears. Inference for zero-inflated count data has gathered much attention in a wide range of applied areas. We present results for both estimation and prediction of Poisson models with zero inflation. We investigate the asymptotic minimax risk that indicates a clear correspondence between Gaussian and Poisson models with sparsity. An easy-implemented asymptotically minimax estimator is constructed using a spike-and-slab prior with a polynomially-decaying slab prior. We also investigate asymptotically minimax predictive densities that are adaptive to an unknown sparsity level. To achieve this result, we have employed a new idea of calibrating the scale of the slab prior according to the minimax risk.