Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Estimating the Maximum Expected Value: An Analysis of (Nested) Cross
  Validation and the Maximum Sample Average   We investigate the accuracy of the two most common estimators for the maximum
expected value of a general set of random variables: a generalization of the
maximum sample average, and cross validation. No unbiased estimator exists and
we show that it is non-trivial to select a good estimator without knowledge
about the distributions of the random variables. We investigate and bound the
bias and variance of the aforementioned estimators and prove consistency. The
variance of cross validation can be significantly reduced, but not without
risking a large bias. The bias and variance of different variants of cross
validation are shown to be very problem-dependent, and a wrong choice can lead
to very inaccurate estimates.

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The categories of this paper are: math
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The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
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The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat