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 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.

[1]  Harry Markowitz,et al.  Portfolio Theory: As I Still See It , 2010 .

[2]  Panos M. Pardalos,et al.  Simple measure of similarity for the market graph construction , 2013, Comput. Manag. Sci..

[3]  Fabrizio Lillo,et al.  Correlation, Hierarchies, and Networks in Financial Markets , 2008, 0809.4615.

[4]  Joseph P. Romano,et al.  Generalizations of the familywise error rate , 2005, math/0507420.

[5]  Abraham Wald,et al.  Statistical Decision Functions , 1951 .

[6]  E. Lehmann.  A General Concept of Unbiasedness , 1951 .

[7]  Panos M. Pardalos,et al.  Mining market data: A network approach , 2006, Comput. Oper. Res..

[8]  E. Lehmann.  Testing Statistical Hypotheses , 1960 .

[9]  Rosario N. Mantegna,et al.  Book Review: An Introduction to Econophysics, Correlations, and Complexity in Finance, N. Rosario, H. Mantegna, and H. E. Stanley, Cambridge University Press, Cambridge, 2000. , 2000 .

[10]  T. W. Anderson.  An Introduction to Multivariate Statistical Analysis , 1959 .

[11]  Juliet Popper Shaffer,et al.  Recent developments towards optimality in multiple hypothesis testing , 2006, math/0610841.

[12]  Panos M. Pardalos,et al.  Statistical analysis of financial networks , 2005, Comput. Stat. Data Anal..

[13]  Xintian Zhuang,et al.  A network analysis of the Chinese stock market , 2009 .

[14]  Michael Wolf,et al.  Control of generalized error rates in multiple testing , 2007, 0710.2258.

[15]  R. Mantegna.  Hierarchical structure in financial markets , 1998, cond-mat/9802256.

[16]  Veronica Vinciotti,et al.  Robust methods for inferring sparse network structures , 2013, Comput. Stat. Data Anal..