Statistical procedures for the market graph construction
The statistical analysis of the method of construction of the market graph when considered as a multiple decision statistical procedure is investigated. It is shown that under the condition of additivity of the loss function the method can be optimal in different classes of unbiased multiple statist...
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| Published in | Computational statistics & data analysis Vol. 68; pp. 17 - 29 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
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Elsevier B.V
01.12.2013
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| Abstract | The statistical analysis of the method of construction of the market graph when considered as a multiple decision statistical procedure is investigated. It is shown that under the condition of additivity of the loss function the method can be optimal in different classes of unbiased multiple statistical procedures. The results are obtained by application of the Lehmann theory of multiple decision procedures to the method of construction of the market graph. The main findings are illustrated by numerical studies of the conditional risk of multiple decision statistical procedures for different loss functions and different return distributions.
•The market graph construction is investigated as a multiple decision statistical procedure.•The multiple decision problem is reduced to the family of two-decision problems.•Multiple decision statistical testing is reduced to generating hypothesis testing.•The market graph construction procedure is optimal as a multiple decision statistical procedure.•Compatibility conditions and additivity of the loss function are discussed theoretically and numerically. |
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| AbstractList | The statistical analysis of the method of construction of the market graph when considered as a multiple decision statistical procedure is investigated. It is shown that under the condition of additivity of the loss function the method can be optimal in different classes of unbiased multiple statistical procedures. The results are obtained by application of the Lehmann theory of multiple decision procedures to the method of construction of the market graph. The main findings are illustrated by numerical studies of the conditional risk of multiple decision statistical procedures for different loss functions and different return distributions.
•The market graph construction is investigated as a multiple decision statistical procedure.•The multiple decision problem is reduced to the family of two-decision problems.•Multiple decision statistical testing is reduced to generating hypothesis testing.•The market graph construction procedure is optimal as a multiple decision statistical procedure.•Compatibility conditions and additivity of the loss function are discussed theoretically and numerically. The statistical analysis of the method of construction of the market graph when considered as a multiple decision statistical procedure is investigated. It is shown that under the condition of additivity of the loss function the method can be optimal in different classes of unbiased multiple statistical procedures. The results are obtained by application of the Lehmann theory of multiple decision procedures to the method of construction of the market graph. The main findings are illustrated by numerical studies of the conditional risk of multiple decision statistical procedures for different loss functions and different return distributions. |
| Author | Pardalos, Panos M. Koldanov, Alexander P. Kalyagin, Valeriy A. Koldanov, Petr A. |
| Author_xml | – sequence: 1 givenname: Alexander P. surname: Koldanov fullname: Koldanov, Alexander P. organization: National Research University Higher School of Economics, Bolshaya Pecherskaya 25/12, Nizhny Novgorod, 603155, Russia – sequence: 2 givenname: Petr A. surname: Koldanov fullname: Koldanov, Petr A. organization: National Research University Higher School of Economics, Bolshaya Pecherskaya 25/12, Nizhny Novgorod, 603155, Russia – sequence: 3 givenname: Valeriy A. surname: Kalyagin fullname: Kalyagin, Valeriy A. email: vkalyagin@hse.ru organization: National Research University Higher School of Economics, Bolshaya Pecherskaya 25/12, Nizhny Novgorod, 603155, Russia – sequence: 4 givenname: Panos M. surname: Pardalos fullname: Pardalos, Panos M. organization: National Research University Higher School of Economics, Bolshaya Pecherskaya 25/12, Nizhny Novgorod, 603155, Russia |
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| Cites_doi | 10.1016/j.cor.2005.01.027 10.1016/j.physa.2009.03.028 10.1214/009053606000001622 10.1007/s100510050929 10.1146/annurev-financial-011110-134602 10.1016/j.csda.2013.05.004 10.1214/aoms/1177729549 10.1214/074921706000000374 10.1214/aoms/1177707034 10.1214/009053605000000084 10.1016/j.csda.2004.02.004 10.1016/j.jebo.2010.01.004 10.1007/s10287-013-0169-3 |
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| Keywords | Market graph Multiple decision statistical procedures Unbiased statistical tests Generating hypotheses Additivity of the loss function Conditional risk |
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| References | Bautin, Kalyagin, Koldanov, Koldanov, Pardalos (br000010) 2013 Markowitz (br000065) 1952; 7 Romano, Wolf (br000080) 2007; 35 Lehmann, Romano (br000045) 2005 Anderson (br000005) 2003 Lehmann (br000035) 1951; 22 Lehmann (br000040) 1957; 28 Markowitz (br000070) 2010; 2 Rao, Swarupchand (br000075) 2009; 16 Boginsky, Butenko, Pardalos (br000020) 2005; 48 Wald (br000100) 1950 Lehmann, Romano (br000050) 2005; 33 Boginsky, Butenko, Pardalos (br000015) 2003 Mantegna (br000055) 1999; 11 Vinciotti, Hashem (br000095) 2013; 67 Huang, Zhuang, Shuang (br000030) 2009; 388 Shaffer (br000085) 2006; 49 Tumminello, Lillo, Mantegna (br000090) 2010; 75 Boginsky, Butenko, Pardalos (br000025) 2006; 33 Mantegna, Stanley (br000060) 2000 Wald (10.1016/j.csda.2013.06.005_br000100) 1950 Lehmann (10.1016/j.csda.2013.06.005_br000040) 1957; 28 Lehmann (10.1016/j.csda.2013.06.005_br000035) 1951; 22 Shaffer (10.1016/j.csda.2013.06.005_br000085) 2006; 49 Boginsky (10.1016/j.csda.2013.06.005_br000015) 2003 Tumminello (10.1016/j.csda.2013.06.005_br000090) 2010; 75 Bautin (10.1016/j.csda.2013.06.005_br000010) 2013 Anderson (10.1016/j.csda.2013.06.005_br000005) 2003 Lehmann (10.1016/j.csda.2013.06.005_br000050) 2005; 33 Huang (10.1016/j.csda.2013.06.005_br000030) 2009; 388 Boginsky (10.1016/j.csda.2013.06.005_br000025) 2006; 33 Markowitz (10.1016/j.csda.2013.06.005_br000070) 2010; 2 Markowitz (10.1016/j.csda.2013.06.005_br000065) 1952; 7 Boginsky (10.1016/j.csda.2013.06.005_br000020) 2005; 48 Mantegna (10.1016/j.csda.2013.06.005_br000055) 1999; 11 Romano (10.1016/j.csda.2013.06.005_br000080) 2007; 35 Mantegna (10.1016/j.csda.2013.06.005_br000060) 2000 Rao (10.1016/j.csda.2013.06.005_br000075) 2009; 16 Lehmann (10.1016/j.csda.2013.06.005_br000045) 2005 Vinciotti (10.1016/j.csda.2013.06.005_br000095) 2013; 67 |
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| SubjectTerms | Additivity of the loss function Conditional risk Construction Generating hypotheses Market graph Multiple decision statistical procedures Unbiased statistical tests |
| Title | Statistical procedures for the market graph construction |
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