Risk function and optimality of statistical procedures for identification of network structures
Identification of network structures using the finite-size sample has been considered. The concepts of random variables network and network model, which is a complete weighted graph, have been introduced. Two types of network structures have been investigated: network structures with an arbitrary nu...
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| Format: | Article |
| Language: | English |
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Kazan Federal University
2018-06-01
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| Series: | Учёные записки Казанского университета: Серия Физико-математические науки |
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| Online Access: | https://kpfu.ru/risk-function-and-optimality-of-statistical-403652.html |
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| _version_ | 1841563217537531904 |
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| author | P.A. Koldanov |
| author_facet | P.A. Koldanov |
| author_sort | P.A. Koldanov |
| collection | DOAJ |
| description | Identification of network structures using the finite-size sample has been considered. The concepts of random variables network and network model, which is a complete weighted graph, have been introduced. Two types of network structures have been investigated: network structures with an arbitrary number of elements and network structures with a fixed number of elements of the network model. The problem of identification of network structures has been investigated as a multiple testing problem. The risk function of statistical procedures for identification of network structures can be represented as a linear combination of expected numbers of incorrectly included elements and incorrectly non-included elements. The sufficient conditions of optimality for statistical procedures for network structures identification with an arbitrary number of elements have been given. The concept of statistical uncertainty of statistical procedures for identification of network structures has been introduced. |
| format | Article |
| id | doaj-art-6786e13f3e664fa6aa8f2f55d58dbba8 |
| institution | Kabale University |
| issn | 2541-7746 2500-2198 |
| language | English |
| publishDate | 2018-06-01 |
| publisher | Kazan Federal University |
| record_format | Article |
| series | Учёные записки Казанского университета: Серия Физико-математические науки |
| spelling | doaj-art-6786e13f3e664fa6aa8f2f55d58dbba82025-01-03T00:06:23ZengKazan Federal UniversityУчёные записки Казанского университета: Серия Физико-математические науки2541-77462500-21982018-06-011602317326Risk function and optimality of statistical procedures for identification of network structuresP.A. Koldanov0National Research University Higher School of Economics, Nizhny Novgorod, 603025 RussiaIdentification of network structures using the finite-size sample has been considered. The concepts of random variables network and network model, which is a complete weighted graph, have been introduced. Two types of network structures have been investigated: network structures with an arbitrary number of elements and network structures with a fixed number of elements of the network model. The problem of identification of network structures has been investigated as a multiple testing problem. The risk function of statistical procedures for identification of network structures can be represented as a linear combination of expected numbers of incorrectly included elements and incorrectly non-included elements. The sufficient conditions of optimality for statistical procedures for network structures identification with an arbitrary number of elements have been given. The concept of statistical uncertainty of statistical procedures for identification of network structures has been introduced.https://kpfu.ru/risk-function-and-optimality-of-statistical-403652.htmlrandom variables networknetwork modelnetwork structureprocedure for identification of network structureadditive loss functionrisk functionunbiasednessoptimalitystatistical uncertainty |
| spellingShingle | P.A. Koldanov Risk function and optimality of statistical procedures for identification of network structures Учёные записки Казанского университета: Серия Физико-математические науки random variables network network model network structure procedure for identification of network structure additive loss function risk function unbiasedness optimality statistical uncertainty |
| title | Risk function and optimality of statistical procedures for identification of network structures |
| title_full | Risk function and optimality of statistical procedures for identification of network structures |
| title_fullStr | Risk function and optimality of statistical procedures for identification of network structures |
| title_full_unstemmed | Risk function and optimality of statistical procedures for identification of network structures |
| title_short | Risk function and optimality of statistical procedures for identification of network structures |
| title_sort | risk function and optimality of statistical procedures for identification of network structures |
| topic | random variables network network model network structure procedure for identification of network structure additive loss function risk function unbiasedness optimality statistical uncertainty |
| url | https://kpfu.ru/risk-function-and-optimality-of-statistical-403652.html |
| work_keys_str_mv | AT pakoldanov riskfunctionandoptimalityofstatisticalproceduresforidentificationofnetworkstructures |