Asymptotic Normality of Semiparametric and Nonparametric Posterior Distributions

By Xiaotong Shen. 2002

89 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

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Citations in the corpus

Finite Sample Bernstein -- von Mises Theorem for Semiparametric Problems (2013, background): “Asymptotic normality of the posterior measure for these classes of models is even more challenging; see e.g. Shen (2002).”
Bernstein - von Mises Theorem for growing parameter dimension (2013, background): “…the i.i.d. case; Ghosal (1999), Ghosal (2000) for high dimensional linear models; Boucheron and Gassiat (2009), Kim (2006) for non-Gaussian models; Shen (2002), Bickel and Kleijn (2012), and Castillo (2012) for the semiparametric version of the BvM result; Kleijn and van der Vaart (2006), Bunke…”
Convergence rates of posterior distributions for non-i.i.d. observations (2007, background): “The posterior of the Euclidean part is also expected to converge at an n~1/2 rate and the Bernstein-von Mises theorem may hold; see [26] for some results.”
The semiparametric Bernstein-von Mises theorem (2010, background): “A general approach has been given in Shen [39], but his conditions may prove somewhat hard to verify in examples.”
High dimensional Bernstein-von Mises: simple examples (2010, methodology): “In a semiparametric setting, where a finite dimensional parameter of interest can be separated from an infinite dimensional nuisance parameter, Castillo [3] obtains conditions leading to a Bernstein-von Mises theorem on the parametric part, clarifying an earlier work of Shen [20].”
Dirichlet Process Mixtures of Generalized Linear Models (2009, background): “osterior convergence in the models where L1 or Hellinger consistency has been shown (Ghosal et al. 2000, Shen & Wasserman 2001, Walker et al. 2007, Ghosal & van der Vaart 2007). More broadly, Shen (2002) gave conditions for asymptotic normality of nonparametric functionals, but required fair”
Critical dimension in the semiparametric Bernstein—von Mises theorem (2014, unknown): “, [26]).”
The Bernstein–von Mises theorem for the proportional hazard model (2006, background): “MR0139190 [22] Shen, X. (2002).”
Bernstein von Mises Theorems for Gaussian Regression with increasing number of regressors (2010, background): “It clarifies a preceding paper [15], which considers also the more general framework where the quantity of interest is a finite-dimensional function g(f) of the infinite-dimensional parameter f of the model.”
Bayesian inference in a class of partially identified models (2016, background): “There is a function of the data µ n ( X ) and a covariance matrix Σ 0 such that, along almost all sample sequences, This assumption is essentially the conclusion of the various “Bernstein-von Mises”-like theorems for a point identiﬁed parameter (e.g., Van der Vaart (1998), Shen (2002), or Bickel and”
Noname manuscript No. (will be inserted by the editor) A semiparametric Bernstein- von Mises theorem for Gaussian process priors (unknown): “We do not have to deal with a nonparametric θ̂M L E , which would in this example turn the study of the gn(θ̂) in [24] even more complex, even putting aside the fact that no direct computations of the integrated likelihood seem possible for the considered model and prior, at least in a simple way.”
BERNSTEIN-VON MISES THEOREM FOR LINEAR FUNCTIONALS OF THE DENSITY (2009, methodology): “BVM FOR LINEAR FUNCTIONALS OF THE DENSITY 3 sance parameter, [3] obtains interesting conditions leading to a Bernsteinvon Mises theorem on the parameter of interest, clarifying an earlier work of [20].”
A Bernstein–von Mises theorem for smooth functionals in semiparametric models (2013, methodology): “Results on semiparametric BvM applicable to general models and/or general priors include Shen [31], Castillo [10], Rivoirard and Rousseau [30] and Bickel and Kleijn [3].”
On the Bernstein-von Mises phenomenon in the Gaussian white noise model (2011, background): “, [1, 11, 12] for semiparamatric and [5, 6] for nonparametric, the results in [2] and [3] led to the widely accepted belief that the BvM phenomenon does not occur in the nonparametric framework.”