Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On deconvolution with repeated measurements   In a large class of statistical inverse problems it is necessary to suppose
that the transformation that is inverted is known. Although, in many
applications, it is unrealistic to make this assumption, the problem is often
insoluble without it. However, if additional data are available, then it is
possible to estimate consistently the unknown error density. Data are seldom
available directly on the transformation, but repeated, or replicated,
measurements increasingly are becoming available. Such data consist of
``intrinsic'' values that are measured several times, with errors that are
generally independent. Working in this setting we treat the nonparametric
deconvolution problems of density estimation with observation errors, and
regression with errors in variables. We show that, even if the number of
repeated measurements is quite small, it is possible for modified kernel
estimators to achieve the same level of performance they would if the error
distribution were known. Indeed, density and regression estimators can be
constructed from replicated data so that they have the same first-order
properties as conventional estimators in the known-error case, without any
replication, but with sample size equal to the sum of the numbers of
replicates. Practical methods for constructing estimators with these properties
are suggested, involving empirical rules for smoothing-parameter choice.

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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
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The categories of this paper are: q-bio
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The categories of this paper are: physics
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The categories of this paper are: econ
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The categories of this paper are: plasm-ph
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The categories of this paper are: supr-con
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The categories of this paper are: hep-th
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The categories of this paper are: cs
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int