When the degree sequence is a sufficient statistic

V. Csiszár; Péter Hussami; János Komlós; Tamás F. Móri; Lídia Rejto; Gábor Tusnády

doi:10.1007/s10474-011-0125-z

When the degree sequence is a sufficient statistic

V. Csiszár, Péter Hussami, János Komlós, Tamás F. Móri, Lídia Rejto, Gábor Tusnády

School of Arts and Sciences, Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

There is a uniquely defined random graph model with independent adjacencies in which the degree sequence is a sufficient statistic. The model was recently discovered independently by several authors. Here we join to the statistical investigation of the model, proving that if the degree sequence is in the interior of the polytope defined by the Erdo{double acute}s-Gallai conditions, then a unique maximum likelihood estimate exists.

Original language	English (US)
Pages (from-to)	45-53
Number of pages	9
Journal	Acta Mathematica Hungarica
Volume	134
Issue number	1-2
DOIs	https://doi.org/10.1007/s10474-011-0125-z
State	Published - Jan 2012

All Science Journal Classification (ASJC) codes

Mathematics(all)

Keywords

degree sequence of graphs
maximum likelihood estimation
random graph
sufficient statistics

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10.1007/s10474-011-0125-z

Cite this

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title = "When the degree sequence is a sufficient statistic",

abstract = "There is a uniquely defined random graph model with independent adjacencies in which the degree sequence is a sufficient statistic. The model was recently discovered independently by several authors. Here we join to the statistical investigation of the model, proving that if the degree sequence is in the interior of the polytope defined by the Erdo{double acute}s-Gallai conditions, then a unique maximum likelihood estimate exists.",

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author = "V. Csisz{\'a}r and P{\'e}ter Hussami and J{\'a}nos Koml{\'o}s and M{\'o}ri, {Tam{\'a}s F.} and L{\'i}dia Rejto and G{\'a}bor Tusn{\'a}dy",

note = "Funding Information: ∗Supported by the European Union and the European Social Fund under the grant agreement no. T{\'A}MOP 4.2.1./B-09/KMR-2010-0003. †Supported by OTKA grant K 76481. ‡Supported by OTKA grant K 67961. §Supported in part by NSF grant DMS-0902241. ¶Corresponding author. Key words and phrases: degree sequence of graphs, random graph, sufficient statistics, maximum likelihood estimation. 2000 Mathematics Subject Classification: primary 62F10, secondary 05C07.",

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doi = "10.1007/s10474-011-0125-z",

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AU - Csiszár, V.

AU - Hussami, Péter

AU - Komlós, János

AU - Móri, Tamás F.

AU - Rejto, Lídia

AU - Tusnády, Gábor

N1 - Funding Information: ∗Supported by the European Union and the European Social Fund under the grant agreement no. TÁMOP 4.2.1./B-09/KMR-2010-0003. †Supported by OTKA grant K 76481. ‡Supported by OTKA grant K 67961. §Supported in part by NSF grant DMS-0902241. ¶Corresponding author. Key words and phrases: degree sequence of graphs, random graph, sufficient statistics, maximum likelihood estimation. 2000 Mathematics Subject Classification: primary 62F10, secondary 05C07.

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N2 - There is a uniquely defined random graph model with independent adjacencies in which the degree sequence is a sufficient statistic. The model was recently discovered independently by several authors. Here we join to the statistical investigation of the model, proving that if the degree sequence is in the interior of the polytope defined by the Erdo{double acute}s-Gallai conditions, then a unique maximum likelihood estimate exists.

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When the degree sequence is a sufficient statistic

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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