Uniformity and the Delta Method
By Maximilian Kasy. 2015
35 citations recorded by the source corpus.
Abstract When are asymptotic approximations using the delta-method uniformly valid? We provide sufficient conditions as well as closely related necessary conditions for uniform negligibility of the remainder of such approximations. These conditions are easily verified by empirical practitioners and permit to identify settings and parameter regions where pointwise asymptotic approximations perform poorly. Our framework allows for a unified and transparent discussion of uniformity issues in various sub-fields of statistics and econometrics. Our conditions involve uniform bounds on the remainder of a first-order approximation for the function of interest.
Subfields: Economics and Econometrics, Statistics and Probability
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In Economics and Econometrics
- Jan Peters
- Alessandro Rinaldo
- Larry A. Wasserman
- Robert Tibshirani
- Rajen Dinesh Shah
- Richard S. Sutton
In Statistics and Probability
- Jan Peters
- Robert Tibshirani
- Peter Buhlmann
- Larry A. Wasserman
- Rajen Dinesh Shah
- Alessandro Rinaldo
- E.J. Candes
- Bernhard Schölkopf
Citations in the corpus
- The hardness of conditional independence testing and the generalised covariance measure (2018, background): “These stronger properties follow easily from the stronger assumptions given in the statement of the result; that they suffice for the uniform central limit theorem is shown in Kasy [30].”
- Uniform asymptotic inference and the bootstrap after model selection (2015, background): “A recent article by Kasy (2015) emphasizes the importance of uniformity in asymptotic approximations.”