YOSHIDA, Nakahiro

Title
 Professor
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.: Asymptotic expansion for statistics related to small diffusions. J. Japan Statist. Soc. 22, 139-159 (1992).
  3. Yoshida, N.: Estimation for diffusion processes from discrete observation, J. Multivariate Analysis, 41, 220-242 (1992).
  4. Yoshida, N.: Asymptotic expansion of Bayes estimators for small diffusions, Probab. Theory Related Fields, 95 , 429-450 (1993).
  5. Yoshida, N.: Malliavin calculus and asymptotic expansion for martingales, Probab. Theory Related Fields, 109, 301-342 (1997).
  6. Kusuoka, S., Yoshida, N.: Malliavin calculus, strong mixing, and expansion of diffusion functionals. Prob. Theory Related Fields 116, 457-484 (2000).
  7. Sakamoto, Y., Yoshida, N.: Asymptotic expansion formulas for functionals of epsilon-Markov processes with a mixing property. Annals of the Institute of Statistical Mathematics, 56, 545-597 (2004).
  8. Yoshida, N.: Partial mixing and conditional Edgeworth expansion for diffusions with jumps. Probab. Theory Related Fields 129, 559-624 (2004).
  9. Hayashi, T., Yoshida, N.: On covariance estimation of nonsynchronously observed diffusion processes. Bernoulli, 11, 359-379 (2005).
  10. Shimizu, Y., Yoshida, N.: Estimation of parameters for diffusion processes with jumps from discrete observations. Stat. Inferecne Stoch. Process., 9, 227-277 (2006).
  11. Hayashi, T., Yoshida, N.: Asymptotic normality of a covariance estimator for nonsynchronously observed diffusion processes, Annals of the Institute of Statistical Mathematics 60, 367-406 (2008).
  12. Sakamoto, Y., Yoshida, N.: Third-order asymptotic expansion of M-estimators for diffusion processes, Annals of the Institute of Statistical Mathematics 61, 629-661 (2009).
  13. Yoshida, N. : Polynomial type large deviation inequalities and quasi-likelihood analysis for stochastic differential equations, Annals of the Institute of Statistical 63, 3, 431-479 (2011).
  14. Hayashi, T., Yoshida, N.: Nonsynchronous covariation process and limit theorems, Stochastic Processes and their Applications, 121, 10, 2416-2454 (2011).
  15. Ogihara, T., Yoshida, N.: Quasi-likelihood analysis for the stochastic differential equation with jumps, Statistical Inference for Stochastic Processes, 14, 3, 189-229 (2011).
  16. Uchida, M., Yoshida, N.: Adaptive estimation of an ergodic diffusion process based on sampled data, Stochastic Processes and their Applications, 122, 8, 2885-2924 (2012).
  17. Yoshida, N.: Martingale expansion in mixed normal limit, Stochastic Processes and their Applications, 123, 3, 887-933 (2013).
  18. Uchida, M., Yoshida, N.: Quasi likelihood analysis of volatility and nondegeneracy of statistical random field, Stochastic Processes and their Applications, 123, 7, 2851-2876 (2013).
  19. YUIMA Project Team: The YUIMA Project: A Computational framework for simulation and inference of stochastic differential equations, Journal of Statistical Software, 57, 4, 1-51 (2014).
  20. Podolskij, M., Yoshida, N.: Edgeworth expansion for functionals of continuous diffusion processes, Annals of Applied Probability, 26, 6, 3415-3455 (2016).
  21. Muni Toke, I., Yoshida, N.: Modelling intensities of order flows in a limit order book, Quantitative Finance, 17, 5, 683-701 (2017).
  22. Podolskij, M., Veliyev, B., Yoshida, N.: Edgeworth expansion for the pre-averaging estimator, Stochastic Processes and their Applications, 127, 11, 3558-3595 (2017).
  23. Tudor, C., Yoshida, N.: Asymptotic expansion for vector-valued sequences of random variables with focus on Wiener chaos, Stochastic Processes and their Applications, 129, 9, 3499-3526 (2019).
  24. Nualart, D., Yoshida, N.: Asymptotic expansion of Skorohod integrals, Electron. J. Probab., 24, paper no. 119, 64 pp. (2019).
  25. Gloter, A., Yoshida, N.: Adaptive estimation for degenerate diffusion processes. Electronic Journal of Statistics, 15(1), 1424-1472 (2021)
  26. Tudor, Ciprian A., Yoshida, N.: High order asymptotic expansion for Wiener functionals. Stochastic Processes and their Applications, 164, 443-492 (2023)
  27. Yoshida, N.: Asymptotic expansion and estimates of Wiener functionals. Stochastic Processes and their Applications, 157, 176-248 (2023)
Memberships, awards and activities

Mathematical Society of Japan, Japan Statistical Society, International Statistical Institute, Bernoulli Society. The 2024 Mathematical Society of Japan Autumn Prize (2024), Hiroshi Fujiwara Prize for Mathematical Sciences (2019), 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