Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bayes and maximum likelihood for $L^1$-Wasserstein deconvolution of
  Laplace mixtures   We consider the problem of recovering a distribution function on the real
line from observations additively contaminated with errors following the
standard Laplace distribution. Assuming that the latent distribution is
completely unknown leads to a nonparametric deconvolution problem. We begin by
studying the rates of convergence relative to the $L^2$-norm and the Hellinger
metric for the direct problem of estimating the sampling density, which is a
mixture of Laplace densities with a possibly unbounded set of locations: the
rate of convergence for the Bayes' density estimator corresponding to a
Dirichlet process prior over the space of all mixing distributions on the real
line matches, up to a logarithmic factor, with the $n^{-3/8}\log^{1/8}n$ rate
for the maximum likelihood estimator. Then, appealing to an inversion
inequality translating the $L^2$-norm and the Hellinger distance between
general kernel mixtures, with a kernel density having polynomially decaying
Fourier transform, into any $L^p$-Wasserstein distance, $p\geq1$, between the
corresponding mixing distributions, provided their Laplace transforms are
finite in some neighborhood of zero, we derive the rates of convergence in the
$L^1$-Wasserstein metric for the Bayes' and maximum likelihood estimators of
the mixing distribution. Merging in the $L^1$-Wasserstein distance between
Bayes and maximum likelihood follows as a by-product, along with an assessment
on the stochastic order of the discrepancy between the two estimation
procedures.

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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ph
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The categories of this paper are: econ
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: cs
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The categories of this paper are: math
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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph