Bitte verwenden Sie diesen Link, um diese Publikation zu zitieren, oder auf sie als Internetquelle zu verweisen: https://hdl.handle.net/10419/149766 
Erscheinungsjahr: 
2016
Schriftenreihe/Nr.: 
cemmap working paper No. CWP20/16
Verlag: 
Centre for Microdata Methods and Practice (cemmap), London
Zusammenfassung: 
This paper examines the asymptotic behavior of the posterior distribution of a possibly nondifferentiable function g(theta), where is a finite dimensional parameter. The main assumption is that the distribution of the maximum likelihood estimator theta_n, its bootstrap approximation, and the Bayesian posterior for 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 g(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 the posterior distribution of g(theta) does not coincide with the asymptotic distribution of g(theta_n) at points of nondifferentiability. Consequently, frequentists cannot presume that credible sets for a nondifferentiable parameter g(theta) can be interpreted as approximately valid confidence sets (even when this relation holds true for theta).
Schlagwörter: 
Bootstrap
Bernstein von-Mises Theorem
Directional Differentiability
Posterior Inference
Persistent Identifier der Erstveröffentlichung: 
Dokumentart: 
Working Paper

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