Adaptive Test of Conditional Moment Inequalities

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In this paper, I construct a new test of conditional moment inequalities, which is based on studentized kernel estimates of moment functions with many different values of the bandwidth parameter.

• The test automatically adapts to the unknown smoothness of moment functions and has uniformly correct asymptotic size.
• The test has high power in a large class of models with conditional moment inequalities.
• Some existing tests have nontrivial power against n^{-1/2}-local alternatives in a certain class of these models whereas my method only allows for nontrivial testing against (n/\log n)^{-1/2}-local alternatives in this class.