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Uniform confidence bands: Characterization and optimality
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DOI：10.1016/j.jeconom.2018.01.006.png)
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This paper studies optimal uniform confidence bands for functions g(x, beta(0)), where beta(0) is an unknown parameter vector. We provide a simple characterization of a general class of taut 1-alpha uniform confidence bands, allowing for both nonlinear functions and nonparametrically estimated functions. Specifically, we show that all taut bands can be obtained from projections on confidence sets for beta(0) and we characterize the class of sets which yield taut bands. Using these results, we then present a computational method for selecting an approximately optimal confidence band for a given objective function. We illustrate the applicability of these results in numerical applications. (C) 2018 Elsevier B.V. All rights reserved.
Keyword:
Uniform confidence bands
Simultaneous inference
Projections
Optimality
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