Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized Estimating Equation for the Student-t Distributions   In \cite{KumarS15J2}, it was shown that a generalized maximum likelihood
estimation problem on a (canonical) $\alpha$-power-law model
($\mathbb{M}^{(\alpha)}$-family) can be solved by solving a system of linear
equations. This was due to an orthogonality relationship between the
$\mathbb{M}^{(\alpha)}$-family and a linear family with respect to the relative
$\alpha$-entropy (or the $\mathscr{I}_\alpha$-divergence). Relative
$\alpha$-entropy is a generalization of the usual relative entropy (or the
Kullback-Leibler divergence). $\mathbb{M}^{(\alpha)}$-family is a
generalization of the usual exponential family. In this paper, we first
generalize the $\mathbb{M}^{(\alpha)}$-family including the multivariate,
continuous case and show that the Student-t distributions fall in this family.
We then extend the above stated result of \cite{KumarS15J2} to the general
$\mathbb{M}^{(\alpha)}$-family. Finally we apply this result to the Student-t
distribution and find generalized estimators for its parameters.

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The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
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The categories of this paper are: econ
31
The categories of this paper are: ao-sci
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The categories of this paper are: eess
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: hep-th
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The categories of this paper are: q-bio
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom