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CWP441717.pdf
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This paper examines the asymptotic behavior of the posterior distribution of a possibly nondifferentiable function g(theta), where theta is a finite-dimensional parameter of either a parametric or semiparametric model. The main assumption is that the distribution of a suitable estimator theta_n, its bootstrap approximation, and the Bayesian posterior for theta all agree asymptotically.
It is shown that whenever g is Lipschitz, though not necessarily differentiable, the posterior distribution of g(theta) and the bootstrap distribution of theta_n coincide asymptotically. One implication is that Bayesians can interpret bootstrap inference for g(theta) as approximately valid posterior inference in a large sample. Another implication---built on known results about bootstrap inconsistency---is that credible sets for a nondifferentiable parameter g(theta) cannot be presumed to be approximately valid confidence sets (even when this relation holds true for theta).
Authors
![Toru Kitagawa](/sites/default/files/styles/square_desktop/public/2022-05/Toru_Kitagawa.jpg?itok=3kinno1S)
Research Associate University College London and Brown University
Toru is a Research Associate of the IFS, a Professor of Economics at UCL and an Associate Professor in the Department of Economics at Brown University
![Person graphic](/sites/default/files/styles/square_desktop/public/2022-06/IFS-person-graphic.png?itok=hWCtTSrz)
Jose Luis Montiel Olea
![Person graphic](/sites/default/files/styles/square_desktop/public/2022-06/IFS-person-graphic.png?itok=hWCtTSrz)
Jonathan Payne
Working Paper details
- DOI
- 10.1920/wp.cem.2017.4417
- Publisher
- The IFS
Suggested citation
T, Kitagawa and J, Montiel Olea and J, Payne. (2017). Posterior distribution of nondifferentiable functions. London: The IFS. Available at: https://ifs.org.uk/publications/posterior-distribution-nondifferentiable-functions (accessed: 30 June 2024).
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