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This paper develops methods of inference for nonparametric and semiparametric parameters deﬁned by conditional moment inequalities and/or equalities. The parameters need not be identiﬁed. Conﬁdence sets and tests are introduced. The correct uniform asymptotic size of these procedures is established. The false coverage probabilities and power of the CS’s and tests are established for ﬁxed alternatives and some local alternatives. Finite-sample simulation results are given for a nonparametric conditional quantile model with censoring and a nonparametric conditional treatment eﬀect model. The recommended CS/test uses a Cramér-von-Mises-type test statistic and employs a generalized moment selection critical value.
Andrews, Donald W.K. and Shi, Xiaoxia, "Nonparametric Inference Based on Conditional Moment Inequalities" (2011). Cowles Foundation Discussion Papers. 2199.