Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Accurate distribution of X^{T}X with singular, idempotent
  variance-covariance matrix   Assume that X is a set of sample statistics which follow a special case
Central Limit Theorem, namely: as the sample size n increases the corresponding
distribution becomes multivariate Normal with the mean (of each X) equal to
zero and with an idempotent variance-covariance matrix V. It is well known that
X^{T}X has (in the same limit), a chi-squared distribution with degrees of
freedom equal to the trace of V. In this article we extend the above result to
include the corresponding (1/n)-proportional corrections, making the new
approximation substantially more accurate and extending its range of
applicability to small-size samples.

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The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs