Weighted KS Statistics for Inference on Conditional Moment Inequalities

By T. Armstrong. 2011

76 citations recorded by the source corpus.

This paper proposes confidence regions for the identified set in conditional moment inequality models using Kolmogorov-Smirnov statistics with a truncated inverse variance weighting with increasing truncation points. The new weighting differs from those proposed in the literature in two important ways. First, confidence regions based on KS tests with the weighting function I propose converge to the identified set at a faster rate than existing procedures based on bounded weight functions in a broad class of models. This provides a theoretical justification for inverse variance weighting in this context, and contrasts with analogous results for conditional moment equalities in which optimal weighting only affects the asymptotic variance. Second, the new weighting changes the asymptotic behavior, including the rate of convergence, of the KS statistic itself, requiring a new asymptotic theory in choosing the critical value, which I provide. To make these comparisons, I derive rates of convergence for the confidence regions I propose along with new results for rates of convergence of existing estimators under a general set of conditions. A series of examples illustrates the broad applicability of the conditions. A monte carlo study examines the finite sample behavior of the confidence regions.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/1e543409dd59211da6331208383beb711df9d886

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Citations in the corpus

Asymptotically exact inference in conditional moment inequality models (2011, methodology): “The results in this paper relate to recent work on testing conditional moment inequalities, including papers by Andrews and Shi (2013), Kim (2008), Khan and Tamer (2009), Chernozhukov, Lee, and Rosen (2009), Lee, Song, and Whang (2011), Ponomareva (2010), Menzel (2008) and Armstrong (2011). The resu”
Intersection bounds: estimation and inference (2009, background): “Armstrong (2011b) and Chetverikov (2011) both propose interesting and important approaches to estimation and inference based on conditional moment inequalities, which can be seen as introducing full studentization in the procedure of AS, fundamentally changing its behavior.”
TESTING FOR A GENERAL CLASS OF FUNCTIONAL INEQUALITIES (2013, background): “It would be interesting to consider a multiscale version of our test based on a range of bandwidths to see if it achieves adaptive rate-optimality against a sequence of smooth alternatives along the lines of Armstrong and Chan (2013) and Chetverikov (2011).”
TESTING REGRESSION MONOTONICITY IN ECONOMETRIC MODELS (2012, background): “Armstrong, T. (2014) Weighted KS statistics for inference on conditional moment inequalities.”
Monte Carlo Confidence Sets for Identified Sets (2016, unknown): “…see, for example, CHT and Romano and Shaikh (2010) where subsampling based methods are used for general partially-identified models, Bugni (2010) and Armstrong (2014) where bootstrap methods are used for moment inequality models, and Beresteanu and Molinari (2008) where random set methods are used…”
Adaptive test of conditional moment inequalities (2011, methodology): “The other approach (Chernozhukov et al. (2009)), is based on estimating moment functions nonparametrically.”