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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
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
Jose Luis Montiel Olea
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: 29 March 2024).
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