Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-Asymptotic Behavior of the Maximum Likelihood Estimate of a Discrete
  Distribution   In this paper, we study the maximum likelihood estimate of the probability
mass function (pmf) of $n$ independent and identically distributed (i.i.d.)
random variables, in the non-asymptotic regime. We are interested in
characterizing the Neyman--Pearson criterion, i.e., the log-likelihood ratio
for testing a true hypothesis within a larger hypothesis. Wilks' theorem states
that this ratio behaves like a $\chi^2$ random variable in the asymptotic case;
however, less is known about the precise behavior of the ratio when the number
of samples is finite. In this work, we find an explicit bound for the
difference between the cumulative distribution function (cdf) of the
log-likelihood ratio and the cdf of a $\chi^2$ random variable. Furthermore, we
show that this difference vanishes with a rate of order $1/\sqrt{n}$ in
accordance with Wilks' theorem.

3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
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The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
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The categories of this paper are: hep-ex
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
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The categories of this paper are: solv-int