Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The semiparametric Bernstein-von Mises theorem   In a smooth semiparametric estimation problem, the marginal posterior for the
parameter of interest is expected to be asymptotically normal and satisfy
frequentist criteria of optimality if the model is endowed with a suitable
prior. It is shown that, under certain straightforward and interpretable
conditions, the assertion of Le Cam's acclaimed, but strictly parametric,
Bernstein-von Mises theorem [Univ. California Publ. Statist. 1 (1953) 277-329]
holds in the semiparametric situation as well. As a consequence, Bayesian
point-estimators achieve efficiency, for example, in the sense of H\'{a}jek's
convolution theorem [Z. Wahrsch. Verw. Gebiete 14 (1970) 323-330]. The model is
required to satisfy differentiability and metric entropy conditions, while the
nuisance prior must assign nonzero mass to certain Kullback-Leibler
neighborhoods [Ghosal, Ghosh and van der Vaart Ann. Statist. 28 (2000)
500-531]. In addition, the marginal posterior is required to converge at
parametric rate, which appears to be the most stringent condition in examples.
The results are applied to estimation of the linear coefficient in partial
linear regression, with a Gaussian prior on a smoothness class for the
nuisance.

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The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: physics
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: q-alg
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con