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Related papers: The semiparametric Bernstein-von Mises theorem

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We present a criterion for the stochastic completeness of a submanifold in terms of its distance to a hypersurface in the ambient space. This relies in a suitable version of the Hessian comparison theorem. In the sequel we apply a…

Differential Geometry · Mathematics 2013-07-24 G. Pacelli Bessa , Jorge H. de Lira , Adriano A. Medeiros

In this paper, we obtain quantitative, non-asymptotic, and data-dependent \textit{Bernstein-von Mises type} bounds on the normal approximation of the posterior distribution in exponential family models with arbitrary centring and scaling.…

Statistics Theory · Mathematics 2025-01-14 Adrian Fischer , Robert E. Gaunt , Gesine Reinert , Yvik Swan

We study large sample properties of Bayesian analysis of the proportional hazard model with neutral to the right process priors on the baseline hazard function. We show that the posterior distribution of the baseline cumulative hazard…

Statistics Theory · Mathematics 2007-06-13 Yongdai Kim

Asymptotic lower bounds for estimation play a fundamental role in assessing the quality of statistical procedures. In this paper we propose a framework for obtaining semi-parametric efficiency bounds for sparse high-dimensional models,…

Statistics Theory · Mathematics 2017-10-16 Jana Jankova , Sara van de Geer

We consider heteroscedastic nonparametric regression models, when both the mean function and variance function are unknown and to be estimated with nonparametric approaches. We derive convergence rates of posterior distributions for this…

Statistics Theory · Mathematics 2010-10-07 Yuao Hu

This paper studies least-square regression penalized with partly smooth convex regularizers. This class of functions is very large and versatile allowing to promote solutions conforming to some notion of low-complexity. Indeed, they force…

Optimization and Control · Mathematics 2014-07-01 Samuel Vaiter , Gabriel Peyré , Jalal M. Fadili

We study frequentist properties of a Bayesian high-dimensional multivariate linear regression model with correlated responses. The predictors are separated into many groups and the group structure is pre-determined. Two features of the…

Statistics Theory · Mathematics 2019-06-13 Bo Ning , Seonghyun Jeong , Subhashis Ghosal

The nonparametric regression model with normal errors has been extensively studied, both from the frequentist and Bayesian viewpoint. A central result in Bayesian nonparametrics is that under assumptions on the prior, the data-generating…

Statistics Theory · Mathematics 2025-12-24 Paul Rosa

We provide a general theoretical framework to derive Bernstein-von Mises theorems for matrix functionals. The conditions on functionals and priors are explicit and easy to check. Results are obtained for various functionals including…

Statistics Theory · Mathematics 2014-12-02 Chao Gao , Harrison H. Zhou

We propose a scalable variational Bayes method for statistical inference for a single or low-dimensional subset of the coordinates of a high-dimensional parameter in sparse linear regression. Our approach relies on assigning a mean-field…

Machine Learning · Statistics 2025-08-12 Ismaël Castillo , Alice L'Huillier , Kolyan Ray , Luke Travis

The proposed approach extends the confidence posterior distribution to the semi-parametric empirical Bayes setting. Whereas the Bayesian posterior is defined in terms of a prior distribution conditional on the observed data, the confidence…

Methodology · Statistics 2012-05-02 David R. Bickel

The Pitman-Yor process is a random probability distribution, that can be used as a prior distribution in a nonparametric Bayesian analysis. The process is of species sampling type and generates discrete distributions, which yield of the…

Statistics Theory · Mathematics 2021-12-10 S. E. M. P. Franssen , A. W. van der Vaart

Bayesian parameter inference depends on a choice of prior probability distribution for the parameters in question. The prior which makes the posterior distribution maximally sensitive to data is called the Jeffreys prior, and it is…

Cosmology and Nongalactic Astrophysics · Physics 2019-02-25 Steen Hannestad , Thomas Tram

This paper deals with the parametric inference for integrated signals embedded in an additive Gaussian noise and observed at deterministic discrete instants which are not necessarily equidistant. The unknown parameter is multidimensional…

Statistics Theory · Mathematics 2019-03-18 Dominique Dehay , Khalil El Waled , Vincent Monsan

As a competitive alternative to least squares regression, quantile regression is popular in analyzing heterogenous data. For quantile regression model specified for one single quantile level $\tau$, major difficulties of semiparametric…

Methodology · Statistics 2017-05-29 Kani Chen , Yuanyuan Lin , Zhanfeng Wang , Zhiliang Ying

This paper is devoted to the problem of determining the concentration bounds that are achievable in non-parametric regression. We consider the setting where features are supported on a bounded subset of $\mathbb{R}^d$, the regression…

Statistics Theory · Mathematics 2024-12-02 Anna Ben-Hamou , Arnaud Guyader

In this paper, we establish minimax optimal rates of convergence for prediction in a semi-functional linear model that consists of a functional component and a less smooth nonparametric component. Our results reveal that the smoother…

Statistics Theory · Mathematics 2021-11-01 Keli Guo , Jun Fan , Lixing Zhu

Fitted probabilities from widely used Bayesian multinomial probit models can depend strongly on the choice of a base category, which is used to uniquely identify the parameters of the model. This paper proposes a novel identification…

Methodology · Statistics 2020-05-19 Lane F. Burgette , David Puelz , P. Richard Hahn

While nonlinear stochastic partial differential equations arise naturally in spatiotemporal modeling, inference for such systems often faces two major challenges: sparse noisy data and ill-posedness of the inverse problem of parameter…

Numerical Analysis · Mathematics 2019-08-22 Fei Lu , Nils Weitzel , Adam H. Monahan

Parametric stochastic simulators are ubiquitous in science, often featuring high-dimensional input parameters and/or an intractable likelihood. Performing Bayesian parameter inference in this context can be challenging. We present a neural…

Machine Learning · Statistics 2021-10-27 Benjamin Kurt Miller , Alex Cole , Patrick Forré , Gilles Louppe , Christoph Weniger