报告题目：INVERSE REGRESSION PROBLEMS AND APPLICATIONS
报 告 人：田茂再教授 (中国人民大学)
School of Statistics, Renmin University of China
In this talk we consider a sequence of hierarchical space model of inverse problems. The underlying function is estimated from indirect observations over a variety of error distributions including those that are heavy-tailed and may not even possess variances or means. The main contribution of this talk is that we establish some oracle inequalities for the inverse problems by using quantile coupling technique that gives a tight bound for the quantile coupling between an arbitrary sample $p$-quantile and a normal variable, and an automatic selection principle for the nonrandom filters. This leads to the data-driven choice of weights. We also give an algorithm for its implementation. The quantile coupling inequality developed in Theorem 1 is of independent interest, because it includes the median coupling inequality in Theorem 1 of Brown, et al. (2008) as a special case.