Abstract:An established and growing literature on generalized fiducial inference and related fiducial ideas points to the adoption of fiducial inference as a mainstream perspective among modern statisticians. Like Bayesian posteriors, generalized fiducial distributions (GFDs) are known to satisfy Bernstein-von Mises (BvM)-type results under classical regularity conditions. Existing fiducial BvM results, however, rely on relatively restrictive smoothness assumptions and are limited in scope. In this paper, we establish a Bernstein-von Mises theorem for generalized fiducial inference under the general framework of local asymptotic normality, which accommodates non-i.i.d. data settings and reduces to the familiar differentiability in quadratic mean condition in the i.i.d. case. We apply our result to extend existing fiducial theory for free-knot spline models first developed in Sonderegger and Hannig (2014), and further illustrate its generality in models where classical regularity conditions fail or i.i.d. assumptions are not met.
From: J.E. Borgert [view email]
[v1]
Wed, 31 Jan 2024 16:10:52 UTC (34 KB)
[v2]
Thu, 11 Apr 2024 19:12:55 UTC (36 KB)
[v3]
Wed, 24 Apr 2024 20:01:27 UTC (36 KB)
[v4]
Mon, 2 Mar 2026 16:44:08 UTC (439 KB)
[v5]
Wed, 9 Sep 2026 23:02:41 UTC (652 KB)
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