In this article 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 hea...In this article 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 paper 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 this paper is of independent interest,because it includes the median coupling inequality in literature as a special case.展开更多
基金supported by the Major Project of Humanities Social Science Foundation of Ministry of Education(Grant No. 08JJD910247)Key Project of Chinese Ministry of Education (Grant No. 108120)+4 种基金National Natural Science Foundation of China (Grant No. 10871201)Beijing Natural Science Foundation (Grant No. 1102021)the Fundamental Research Funds for the Central Universitiesthe Research Funds of Renmin University of China(Grant No. 10XNL018)the China Statistical Research Project (Grant No. 2011LZ031)
文摘In this article 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 paper 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 this paper is of independent interest,because it includes the median coupling inequality in literature as a special case.
