Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/189768 
Year of Publication: 
2017
Series/Report no.: 
cemmap working paper No. CWP44/17
Publisher: 
Centre for Microdata Methods and Practice (cemmap), London
Abstract: 
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).
Subjects: 
Bootstrap
Bernstein-von Mises Theorem
Directional Differentiability
Posterior Inference
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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