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A Note On Minimax Testing And Confidence Intervals In Moment Inequality Models, Timothy B. Armstrong
A Note On Minimax Testing And Confidence Intervals In Moment Inequality Models, Timothy B. Armstrong
Cowles Foundation Discussion Papers
This note uses a simple example to show how moment inequality models used in the empirical economics literature lead to general minimax relative efficiency comparisons. The main point is that such models involve inference on a low dimensional parameter, which leads naturally to a definition of “distance” that, in full generality, would be arbitrary in minimax testing problems. This definition of distance is justified by the fact that it leads to a duality between minimaxity of confidence intervals and tests, which does not hold for other definitions of distance. Thus, the use of moment inequalities for inference in a low …
On The Choice Of Test Statistic For Conditional Moment Inequalities, Timothy B. Armstrong
On The Choice Of Test Statistic For Conditional Moment Inequalities, Timothy B. Armstrong
Cowles Foundation Discussion Papers
This paper derives asymptotic power functions for Cramer-von Mises (CvM) style tests for conditional moment inequality models in the set identified case. Combined with power results for Kolmogorov-Smirnov (KS) tests, these results can be used to choose the optimal test statistic, weighting function and, for tests based on kernel estimates, kernel bandwidth. The results show that KS tests are preferred to CvM tests, and that a truncated variance weighting is preferred to bounded weightings under a minimax criterion, and for a class of alternatives that arises naturally in these models. The results also provide insight into how moment selection and …
On The Choice Of Test Statistic For Conditional Moment Inequalities, Timothy B. Armstrong
On The Choice Of Test Statistic For Conditional Moment Inequalities, Timothy B. Armstrong
Cowles Foundation Discussion Papers
This paper derives asymptotic approximations to the power of Cramer-von Mises (CvM) style tests for inference on a finite dimensional parameter defined by conditional moment inequalities in the case where the parameter is set identified. Combined with power results for Kolmogorov-Smirnov (KS) tests, these results can be used to choose the optimal test statistic, weighting function and, for tests based on kernel estimates, kernel bandwidth. The results show that, in the setting considered here, KS tests are preferred to CvM tests, and that a truncated variance weighting is preferred to bounded weightings.
On The Choice Of Test Statistic For Conditional Moment Inequalities, Timothy B. Armstrong
On The Choice Of Test Statistic For Conditional Moment Inequalities, Timothy B. Armstrong
Cowles Foundation Discussion Papers
This paper derives asymptotic power functions for Cramer-von Mises (CvM) style tests for inference on a finite dimensional parameter defined by conditional moment inequalities in the case where the parameter is set identified. Combined with power results for Kolmogorov-Smirnov (KS) tests, these results can be used to choose the optimal test statistic, weighting function and, for tests based on kernel estimates, kernel bandwidth. The results show that KS tests are preferred to CvM tests, and that a truncated variance weighting is preferred to bounded weightings under a minimax criterion, and for a class of alternatives that arises naturally in these …