Concentration inequalities, large and moderate deviations for self-normalized empirical processes
Concentration inequalities, large and moderate deviations for self-normalized empirical processes
复制标题
DOI：
10.1214/aop/1039548367
复制
发表时间：
2002-10
影响因子：
2.3
通讯作者：
B. Bercu;E. Gassiat;E. Rio
中科院分区：
文献类型：
--
作者：
B. Bercu;E. Gassiat;E. Rio
We consider the supremum w n of self-normalized empirical processes indexed by unbounded classes of functions F. Such variables are of interest in various statistical applications, for example, the likelihood ratio tests of contamination. Using the Herbst method, we prove an exponential concentration inequality for w n under a second moment assumption on the envelope function of F. This inequality is applied to obtain moderate deviations for w n . We also provide large deviations results for some unbounded parametric classes F.
