We propose a new test for inequalities that is simple and uniformly valid . The test compares the likelihood ratio statistic to a chi-squared critical value, where the degrees of freedom is the rank of the active inequalities . This test requires no tuning parameters or simulations, and therefore is computationally fast , even with many inequalities. Further, it does not require an estimate of the number of binding or close-to-binding inequalities. To show that this test is uniformly valid, we establish a new bound on the probability of translations of cones under the multivariate normal distribution that may be of independent interest. The leading application of our test is inference in moment inequality models. We also consider testing affine inequalities in the multivariate normal model and testing nonlinear inequalities in general asymptotically normal models .
We propose a simple test for moment inequalities that has exact size in normal models with known variance and has uniformly asymptotically exact size more generally . The test compares the quasi-likelihood ratio statistic to a chi-squared critical value, where the degree of freedom is the rank of the inequalities that are active in finite samples. The test requires no simulation and thus is computationally fast and especially suitable for constructing confidence sets for parameters by test inversion. It uses no tuning parameter for moment selection and yet still adapts to the slackness of the moment inequalities. Furthermore, we show how the test can be easily adapted for inference on subvectors for the common empirical setting of conditional moment inequalities with nuisance parameters entering linearly .
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new test for inequalities that is simple and uniformly valid
simple test for moment inequalities that has exact size in normal models with known variance and has uniformly asymptotically exact size more generally
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likelihood
quasi-likelihood
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degrees
degree
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active inequalities . This
inequalities that are active in finite samples. The
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tuning parameters or simulations, and therefore
simulation and thus
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, even with many inequalities. Further, it does not require an estimate of the number of binding or close-to-binding inequalities. To show that this test is uniformly valid, we establish a new bound on the probability of translations of cones under the multivariate normal distribution that may be of independent interest. The leading application of our test is inference in moment inequality models. We also consider testing affine inequalities in the multivariate normal model and testing nonlinear inequalities in general asymptotically normal models
and especially suitable for constructing confidence sets for parameters by test inversion. It uses no tuning parameter for moment selection and yet still adapts to the slackness of the moment inequalities. Furthermore, we show how the test can be easily adapted for inference on subvectors for the common empirical setting of conditional moment inequalities with nuisance parameters entering linearly