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.
 (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.
 (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.
 (statistical data analysis / financial data)
(a) Decomposition of swap interest data in Japan.
(b) Looking into auto-regressive dependence of individual hedge fund
Jureckova, J. “Nonparametric Estimate of Regression Coefficients.” The Annals of Statistics. Vol.47. No.4. 1328-1338, 1971.
R.Miura "Edokko Options: A New Framework of Barrier Options" (with Takahiko Fujita), Asia-Pacific Financial Markets, Vol.9.2, 2002.
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 "A Note on the Principle of Hodges-Lehmann Type Estimation" Keiei Kenkyu, Vol.37, No.5.6, pp. 185-192, January 1987.
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.