4.6 Article

Uniform confidence bands: Characterization and optimality

期刊

JOURNAL OF ECONOMETRICS
卷 204, 期 1, 页码 119-130

出版社

ELSEVIER SCIENCE SA
DOI: 10.1016/j.jeconom.2018.01.006

关键词

Uniform confidence bands; Simultaneous inference; Projections; Optimality

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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.

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