Abstract: We study the problem of testing composite hypotheses versus composite alternatives when there is a slight deviation between the model and the real distribution. The used approach, which we called sub-optimal testing, implies an extension of the initial model and a modification of a sequential statistically significant test for the new model. The sub-optimal test is proposed and a non-asymptotic border for the loss function is obtained. Also we investigate correlation between the sub-optimal test and the sequential probability ratio test for the initial model.

Keywords: statistics, robustness, sequential analysis.

ACM Classification Keywords: G.3 PROBABILITY AND STATISTICS - Nonparametric statistics

Link:

SUB-OPTIMAL NONPARAMETRIC HYPOTHESES DISCRIMINATING WITH GUARANTEED DECISION

Fedor Tsitovich, Ivan Tsitovich

http://www.foibg.com/ijima/vol02/ijima02-01-p06.pdf