Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Randomized Empirical Processes and Confidence Bands via Virtual
  Resampling   Let $X,X_1,X_2,\cdots$ be independent real valued random variables with a
common distribution function $F$, and consider $\{X_1,\cdots,X_N \}$, possibly
a big concrete data set, or an imaginary random sample of size $N\geq 1$ on
$X$. In the latter case, or when a concrete data set in hand is too big to be
entirely processed, then the sample distribution function $F_N$ and the the
population distribution function $F$ are both to be estimated. This, in this
paper, is achieved via viewing $\{X_1,\cdots,X_N \}$ as above, as a finite
population of real valued random variables with $N$ labeled units, and sampling
its indices $\{1,\cdots,N \}$ with replacement $m_N:= \sum_{i=1}^N w_{i}^{(N)}$
times so that for each $1\leq i \leq N$, $w_{i}^{(N)}$ is the count of number
of times the index $i$ of $X_i$ is chosen in this virtual resampling process.
This exposition extends the Doob-Donsker classical theory of weak convergence
of empirical processes to that of the thus created randomly weighted empirical
processes when $N, m_N \rightarrow \infty$ so that $m_N=o(N^2)$.

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The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
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The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th