Kitagawa, T; Montiel Olea, J; Payne, J; Velez, A; (2020) Posterior distribution of nondifferentiable functions. Journal of Econometrics , 217 (1) pp. 161-175. 10.1016/j.jeconom.2019.10.009.

Preview	Text (Article) Kitagawa_Posterior Distribution of Nondifferentiable Functions_AAM.pdf - Accepted Version Download (581kB) | Preview
Preview	Text (Supplementary Material) Kitagawa_Posterior Distribution of Nondifferentiable Functions_SuppM.pdf - Accepted Version Download (778kB) | Preview

Abstract

This paper examines the asymptotic behavior of the posterior distribution of a possibly nondifferentiable function g(θ), where θ is a finite-dimensional parameter of either a parametric or semiparametric model. The main assumption is that the distribution of a suitable estimator θ^n, its bootstrap approximation, and the Bayesian posterior for θ all agree asymptotically. It is shown that whenever g is locally Lipschitz, though not necessarily differentiable, the posterior distribution of g(θ) and the bootstrap distribution of g(θ^n) coincide asymptotically. One implication is that Bayesians can interpret bootstrap inference for g(θ) as approximately valid posterior inference in a large sample. Another implication—built on known results about bootstrap inconsistency—is that credible intervals for a nondifferentiable parameter g(θ) cannot be presumed to be approximately valid confidence intervals (even when this relation holds true for θ).

Download activity - last month

Export as CSVJSONXML

Download activity - last 12 months

Export as JSONXMLCSV

Downloads by country - last 12 months

Export as CSVXMLJSON

Archive Staff Only

View Item