Abstract
Stock selection by Sharp ratio is considered in the framework of multiple statistical hypotheses testing theory. The main attention is paid to comparison of Holm step down and Hochberg step up procedures for different loss functions. Comparison is made on the basis of conditional risk as a function of selection threshold. This approach allows to discover that properties of procedures depend not only on relationship between test statistics, but also depend on dispersion of Sharp ratios. Difference in error rate between two procedures is increasing when the concentration of Sharp ratios is increasing. When Sharp ratios do not have a concentration points there is no significant difference in quality of both procedures.
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References
Boginski, V., Butenko, S., Pardalos, P.M.: Statistical analysis of financial networks. Comput. Stat. Data Anal. 48(2), 431–443 (2005)
Cai, G., Sarkar, S.K.: Modified Simes’ critical values under positive dependence. J. Stat. Plann. Infer. 136, 4129–4146 (2006)
Cai, G., Sarkar, S.K.: Modified Simes’ critical values under independence. Stat. Probab. Lett. 78, 1362–1368 (2008)
Holm, S.: A simple sequentially rejective multiple test procedure. Scand. J. Stat. 6, 65–70 (1979)
Hochberg, Y.: A sharper Bonferroni procedure for multiple tests of significance. Biometrika 75, 800–802 (1988)
Hochberg, Y., Tamhane, A.: Multiple Comparison Procedures. John Wiley and Sons, New York (1987)
Huang, Y., Hsu, J.C.: Hochberg’s step-up method: cutting corners off holm’s step-down method. Biometrika 94(4), 965–975 (2007)
Koldanov, P.A., Bautin, G.A.: Multiple decision problem for stock selection in market network. In: Pardalos, P.M., Resende, M., Vogiatzis, C., Walteros, J. (eds.) Learning and Intelligent Optimization. LNCS, vol. 8426, pp. 98–110. Springer, Heidelberg (2014)
Koldanov, P.A., Kalyagin, V.A., Bautin, G.A.: On some statistical procedures for stock selection problem. Ann. Math. Artif. Intell. doi:10.1007/s10472-014-9447-1
Kalyagin, V.A., Koldanov, P.A., Koldanov, A.P., Zamaraev, V.A.: Market graph and markowitz model. In: Rassias, T.M., Floudas, C.A., Butenko, S. (eds.) Optimization in Science and Engineering (In Honor of the 60th Birthday of Panos M. Pardalos), pp. 293–306. Springer Science+Business Media, New York (2014)
Koldanov, A.P., Koldanov, P.A., Kalyagin, V.A., Pardalos, P.M.: Statistical procedures for the market graph construction. Comput. Stat. Data Anal. 68, 17–29 (2013)
Lehmann, E.L.: A theory of some multiple decision procedures 1. Ann. Math. Stat. 28, 1–25 (1957)
Lehmann, E.L., Romano, J.P.: Testing Statistical Hypotheses. Springer, New York (2005)
Rao, C.V., Swarupchand, U.: Multiple comparison procedures - a note and a bibliography. J. Stat. 16, 66–109 (2009)
Sarkar, S.K., Chang, C.K.: The simes method for multiple testing with positively dependent test statistics. J. Am. Stat. Assoc. 92(440), 1601–1608 (1997)
Acknowledgement
The authors are partly supported by National Research University Higher School of Economics, Russian Federation Government grant, N. 11.G34.31. 0057 and RFFI grant 14-01-00807.
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Koldanov, A.P., Kalyagin, V.A., Pardalos, P.M. (2015). Step Down and Step Up Statistical Procedures for Stock Selection with Sharp Ratio. In: Pardalos, P., Pavone, M., Farinella, G., Cutello, V. (eds) Machine Learning, Optimization, and Big Data. MOD 2015. Lecture Notes in Computer Science(), vol 9432. Springer, Cham. https://doi.org/10.1007/978-3-319-27926-8_3
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