Open AccessInference for subvectors and other functions of partially identified parameters in moment inequality models
Author(s) -
Bugni Federico A.,
Canay Ivan A.,
Shi Xiaoxia
Publication year - 2017
Publication title -
quantitative economics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 4.062
H-Index - 27
eISSN - 1759-7331
pISSN - 1759-7323
DOI - 10.3982/qe490
Subject(s) - inference , moment (physics) , mathematics , projection (relational algebra) , nonlinear system , function (biology) , sample size determination , power (physics) , asymptotic analysis , power function , mathematical optimization , algorithm , computer science , mathematical analysis , statistics , artificial intelligence , physics , classical mechanics , quantum mechanics , evolutionary biology , biology
This paper introduces a bootstrap‐based inference method for functions of the parameter vector in a moment (in)equality model. These functions are restricted to be linear for two‐sided testing problems, but may be nonlinear for one‐sided testing problems. In the most common case, this function selects a subvector of the parameter, such as a single component. The new inference method we propose controls asymptotic size uniformly over a large class of data distributions and improves upon the two existing methods that deliver uniform size control for this type of problem: projection‐based and subsampling inference. Relative to projection‐based procedures, our method presents three advantages: (i) it weakly dominates in terms of finite sample power, (ii) it strictly dominates in terms of asymptotic power, and (iii) it is typically less computationally demanding. Relative to subsampling, our method presents two advantages: (i) it strictly dominates in terms of asymptotic power (for reasonable choices of subsample size), and (ii) it appears to be less sensitive to the choice of its tuning parameter than subsampling is to the choice of subsample size.