We consider the likelihood ratio test of a simple null hypothesis (with density
) against a simple alternative hypothesis (with density
) in the situation that observations
are mismeasured due to the presence of measurement errors. Thus instead of
with unobservable parameter
and unobservable random variable
. When we ignore the presence of measurement errors and perform the original test, the probability of type I error becomes different from the nominal value, but the test is still the most powerful among all tests on the modified level. Further, we derive the minimax test of some families of misspecified hypotheses and alternatives. The test exploits the concept of pseudo-capacities elaborated by Huber and Strassen (1973) and Buja (1986). A numerical experiment illustrates the principles and performance of the novel test.
This is an open access article distributed under the Creative Commons Attribution License
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.