The Bernstein–von Mises theorem for the proportional hazard model

By Yongdai Kim. 2006

62 citations recorded by the source corpus.

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 function and regression coefficients centered at the maximum likelihood estimator is jointly asymptotically equivalent to the sampling distribution of the maximum likelihood estimator.

Subfields: Artificial Intelligence, Finance, Statistics and Probability

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Finance

In Statistics and Probability

Citations in the corpus

Finite Sample Bernstein -- von Mises Theorem for Semiparametric Problems (2013, background): “of the posterior measure for these classes of models is even more challenging; see e.g. Shen (2002). Some results for particular semi and nonparametric problems are available from Kim and Lee (2004); Kim (2006); Leahu (2011); Castillo and Nickl (2013). Cheng and Kosorok (2008) obtained a version of ”
High dimensional Bernstein-von Mises: simple examples (2010, methodology): “In survival analysis, Bernstein-von Mises theorems for the cumulative hazard function are established by Kim and Lee [16] and for the cumulative hazard and fixed dimensional covariate regression parameter in a proportional hazards model in [15].”
Bernstein von Mises Theorems for Gaussian Regression with increasing number of regressors (2010, methodology): “[12] and [11] study the nonparametric right-censoring model and the proportional hazard model.”
Bernstein - von Mises Theorem for growing parameter dimension (2013, background): “…Vaart (2007) for a general theory in 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;…”
A Bernstein–von Mises theorem for smooth functionals in semiparametric models (2013, result): “The variety of possible interactions between prior and model and the subtleties of prior choice are illustrated in the previous general papers and in recent results in specific models such as Kim [24], De Blasi and Hjort [17], Leahu [29], Knapik et al. [26], Castillo [11] and Kruijer and Rousseau [2”
Noname manuscript No. (will be inserted by the editor) A semiparametric Bernstein- von Mises theorem for Gaussian process priors (unknown): “A few semiparametric BVM theorems are known in specific models with wellchosen families of priors, often exploiting the fact that the prior has certain conjugacy properties, see for instance [16], where the author establishes the BVM theorem in the proportional hazards model for Lévy-type priors.”
Critical dimension in the semiparametric Bernstein—von Mises theorem (2014, background): “Some results for particular semi- and nonparametric problems are available in [18, 17, 22, 8].”
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.”
On the Bernstein–von Mises phenomenon for nonparametric Bayes procedures (2013, background): “There exists a Donsker-type BvM theorem for the cumulative distribution function based on Dirichlet process priors, see Lo [31], and this carries over to a variety of closely related nonparametric situations, including quantile inference and censoring models, where Bernstein–von Mises results are av”
BERNSTEIN-VON MISES THEOREM FOR LINEAR FUNCTIONALS OF THE DENSITY (2009, background): “Nice positive results are obtained in [14] and [15], however they rely heavily on a conjugacy property and on the fact that their priors put mass one on discrete probabilities which makes the comparison with the empirical distribution more tractable.”