In this paper, I construct a new test of conditional moment inequalities based on studentized kernel estimates of moment functions. The test automatically adapts to the unknown smoothness of the moment functions, has uniformly correct asymptotic size, and is rate optimal against certain classes of alternatives. Some existing tests have nontrivial power against n-1/2-local alternatives of the certain type whereas my method only allows for nontrivial testing against (n / log n)- 1/2-local alternatives of this type. There exist, however, large classes of sequences of well-bahaved alternatives against which the test developed in this paper is consistent and those tests are not.
Conditional Moment Inequalities Minimax Rate Optimality