Pith. sign in

REVIEW 6 cited by

Bernstein - von Mises Theorem for growing parameter dimension

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1302.3430 v4 pith:ZDO3EFYX submitted 2013-02-14 math.ST stat.TH

Vladimir Spokoiny This is my paper · ORCID
classification math.STstat.TH
keywords dimensionparameterresultsbernsteinfishermisesparticularsample
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
abstract

This paper revisits the prominent Fisher, Wilks, and Bernstein -- von Mises (BvM) results from different viewpoints. Particular issues to address are: nonasymptotic framework with just one finite sample, possible model misspecification, and a large parameter dimension. In particular, in the case of an i.i.d. sample, the mentioned results can be stated for any smooth parametric family provided that the dimension \(p \) of the parameter space satisfies the condition "\(p^{2}/n \) is small" for the Fisher expansion, while the Wilks and the BvM results require "\(p^{3}/n \) is small".

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Robust Data Fusion via Subsampling

    stat.ML 2025-08 conditional novelty 7.0 of 10

    A transfer learning framework with two subsampling strategies (target-guided and leverage-based random sampling) is analyzed, with error bounds showing that selected subsamples of contaminated external data can beat b...

  2. CLT in high-dimensional Bayesian linear regression with low SNR

    math.ST 2025-07 conditional novelty 7.0 of 10

    In low-SNR high-dimensional Bayesian linear regression with product priors, one-dimensional posterior projections and the posterior mean are asymptotically Gaussian, centered at the mean-field approximation, with vari...

  3. On rank estimators in increasing dimensions

    math.ST 2019-08 conditional novelty 7.0 of 10

    For rank-correlation M-estimators with U-process objectives, estimation works at the sqrt(p/n) rate when p/n converges to zero, but normal approximation needs the much stronger condition log(n/p^2) p^{3/2}/n^{1/4} to ...

  4. Distributed and recursive Bayesian inference for Big Data and complex spatio-temporal models

    stat.ME 2026-07 conditional novelty 6.0 of 10

    Distributed and recursive INLA with data-and-latent-field partitioning recovers latent-field posteriors close to full-data inference while cutting cost for large spatio-temporal models.

  5. Factor Augmented Quantile Regression Model

    stat.ME 2025-08 conditional novelty 5.0 of 10

    Factor-augmented quantile regression with convolution smoothing and an ℓ1 penalty is consistent, and a bootstrap test assesses factor-model adequacy.

  6. Stochastic Optimization and Data Science

    math.OC 2026-05 unverdicted novelty 2.0 of 10

    The paper motivates stochastic optimization problems from statistical perspectives and describes offline and online approaches to solve expectation minimization problems.

Pith tools