## M711A Special topics of nonparametric statistics

Faculty of Science
Autumn 2012
Extent and Intensity
2/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: z (credit).
Teacher(s)
Ryozo Miura (lecturer), prof. RNDr. Ivanka Horová, CSc. (deputy)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics - Departments - Faculty of Science
Contact Person: prof. RNDr. Ivanka Horová, CSc.
Supplier department: Department of Mathematics and Statistics - Departments - Faculty of Science
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
This series of lectures aims to introduce some “nonparametric statistics” for Brownian Paths, Generalized Lehmann’s Alternatives (Transformation models) and statistical data analysis for financial data.
Syllabus
• [1] (Probability / Mathematical Finance) Some “nonparametric statistics” for Brownian Paths ( “empirical distribution function of an observed path”, “order statistics of an observed path (this was originally called alpha-quantiles and now called Brownian quantiles) ”, “rank statistics in an observed path”) which have been used for designing exotic derivatives in the literatures of mathematical finance and financial engineering. Some examples of exotic options will be shown as well as other possibilities for applications.
• [2] (Classical Mathematical Statistics./Nonparametrics.) Generalized Lehmann’s Alternatives (Transformation models) in the theory of a classical mathematical statistics in one-sample problem. An on-going trial for a simple linear regression will be discussed as well. We define estimates for parameters in the model derived from rank statistics and discuss asymptotically normality.
• [3] (statistical data analysis / financial data)
• (a) Decomposition of swap interest data in Japan.
• (b) Looking into auto-regressive dependence of individual hedge fund return data.
Literature
• R.Miura "A Note on the Principle of Hodges-Lehmann Type Estimation" Keiei Kenkyu, Vol.37, No.5.6, pp. 185-192, January 1987.
• R.Miura "Decomposition of Japanese Yen Interest Rate Data Through Local Regression."(with R. Shibata), Financial Engineering and the Japanese Markets, Vol.4, No.2, pp. 125-146, 1997.
• R.Miura "A Note on Look-Back Options Based on Order Statistics", Hitotsubashi Journal of Commerce and Management. Vol. 27, No.1, November 1992.
• R.Miura "Edokko Options: A New Framework of Barrier Options" (with Takahiko Fujita), Asia-Pacific Financial Markets, Vol.9.2, 2002.
• R.Miura "On Financial Time Series Decompositions with Applications to Volatility" (with Kjell Doksum and Hiroaki Ymauchi)Hitotsubashi Journal of Commerce and Management, Vol.35, No.1, pp 19-47, October 2000.
• Jureckova, J. “Nonparametric Estimate of Regression Coefficients.” The Annals of Statistics. Vol.47. No.4. 1328-1338, 1971.
Language of instruction
English