YOSHIDA Nakahiro

Field Theoretical Statistics and Probability Theory
Research interests
Asymptotic expansion, limit theorems, statistical inference for stochastic processes, stochastic numerical analysis, applications of statistical methods to finance and insurance mathematics
Current research
I am studying asymptotic expansion for a martingale with mixed normal limit. The expansion formula is written by a certain random symbol specified by the Malliavin calculus. It is applied to approximation of the realized volatility.
Nonsynchronous covariance estimator gives various problems in limit theorems and practical applications to high-frequent data analysis. Asymptotic expansion for pricing options is still our research area. Recently we are developing methods for highly precise tail approximation. We are making YUIMA II, an object-oriented large scale R-software for statistical analysis and simulation for stochastic processes.
Selected publications
  1. Yoshida, N.: Asymptotic expansions of maximum likelihood estimators for small diffusions via the theory of Malliavin-Watanabe, Probab. Theory Related Fields, 92, 275-311 (1992)
  2. Yoshida, N.: Malliavin calculus and asymptotic expansion for martingales, Probab. Theory Related Fields, 109, 301-342 (1997)
  3. Kusuoka, S., Yoshida, N.: Malliavin calculus, strong mixing, and expansion of diffusion functionals. Prob. Theory Related Fields 116, 457-484 (2000)
  4. Yoshida, N.: Partial mixing and conditional Edgeworth expansion for diffusions with jumps. Probab. Theory Related Fields 129, 559-624 (2004)
  5. Yoshida, N.: Estimation for diffusion processes from discrete observation, J. Multivariate Analysis, 41, 220-242 (1992)
  6. Yoshida, N.: Polynomial type large deviation inequality and its applications. Annals of the Institute of Statistical Mathematics on-line (2010)
  7. Uchida, M., Yoshida, N.:Information criteria in model selection for mixing processes. Statistical Inference for Stochastic Processes, 4, 73-98 (2001)
  8. Yoshida, N.: Asymptotic expansion for statistics related to small diffusions.J. Japan Statist. Soc. 22, 139-159 (1992)
  9. Hayashi, T., Yoshida, N.: On covariance estimation of nonsynchronously observed diffusion processes. Bernoulli, 11, 359-379 (2005)
  10. Hayashi, T., Yoshida, N.: Nonsynchronous covariance process and limit theorems. Stochastic Processes and their Applications on-line (2010)
  11. Uchida, M., Yoshida, N.: Adaptive estimation of an ergodic diffusion process based on sampled data. Stochastic Processes and their Appications on-line
Memberships, awards and activities

Mathematical Society of Japan, Japan Statistical Society, International Statistical Institute, Bernoulli Society. Japan Statistical Society Award Japan Statistical Society (2009), The first Research Achievement Award Japan Statistical Society (2007), Analysis Prize Mathematical Society of Japan (2006). Bernoulli Society Executive Committee, Statistical Inference for Stochastic Processes editorial board, ESAIM: Probability and Statistics editorial board, Program committee 8th World Congress in Probability and Statistics 2012 Istanbul, Scientific Program Committee, ISI 59th World Statistics Congress Hong Kong 2013