My research focuses on the statistical modeling of stochastic differential equations (SDEs) based on high-frequency time series data. Specifically, I work to develop a rigorous asymptotic theory for the statistical estimation and hypothesis testing of SDE models, and to construct information criteria for model selection with solid mathematical justification. Additionally, I study the statistical asymptotic theory of stochastic partial differential equations (SPDEs) by leveraging high-frequency spatio-temporal data, with a particular emphasis on developing inference methods for SPDE coefficient parameters and establishing their theoretical foundations. Moreover, I am interested in empirical applications that utilize high-frequency time series and spatio-temporal data, and aim to advance statistical modeling from both theoretical and applied perspectives.

1. Uchida, M. and Yoshida, N.: Information criteria in model selection for mixing processes, Statistical Inference for Stochastic Processes, 4, (2001), 73-98.
2. Sørensen, M. and Uchida, M.: Small-diffusion asymptotics for discretely sampled stochastic differential equations, Bernoulli, 9, (2003), 1051-1069.
3. Uchida, M.: Estimation for dynamical systems with small noise from discrete observations, Journal of the Japan Statistical Society, 33, (2003), 157-167.
4. Uchida, M.: Estimation for discretely observed small diffusions based on approximate martingale estimating functions, Scandinavian Journal of Statistics, 31, (2004), 553-566.
5. Uchida, M: Contrast-based information criterion for ergodic diffusion processes from discrete observations, Annals of the Institute of Statistical Mathematics, 62, (2010), 161-187.
6. Uchida, M. and Yoshida, N.: Adaptive estimation of an ergodic diffusion process based on sampled data, Stochastic Processes and their Applications, 122, (2012), 2885-2924.
7. Kamatani, K. and Uchida, M.: Hybrid multi-step estimators for stochastic differential equations based on sampled data, Statistical Inference for Stochastic Processes, 18, (2015),177-204.
8. Nakakita, S. H. and Uchida, M.: Inference for ergodic diffusions plus noise, Scandinavian Journal of Statistics, 46, (2019), 470-516.
9. Kaino, Y. and Uchida, M.: Adaptive estimator for a parabolic linear SPDE with a small noise, Japanese Journal of Statistics and Data Science, 4, (2021), 513-541.
10. Tonaki, Y. and Uchida, M.: Change point inference in ergodic diffusion processes based on high frequency data, Stochastic Processes and their Applications, 158, (2023), 1-39.
11. Tonaki, Y., Kaino, Y. and Uchida, M.: Parameter estimation for linear parabolic SPDEs in two space dimensions based on high frequency data, Scandinavian Journal of Statistics, 50, (2023), 1568-1589.
12. Kusano, S. and Uchida, M.: Sparse inference of structural equation modeling with latent variables for diffusion processes, Japanese Journal of Statistics and Data Science, 7, (2024), 101-150.
13. Tonaki, Y., Kaino, Y. and Uchida, M.: Parametric estimation for linear parabolic SPDEs in two space dimensions based on temporal and spatial increments, Metrika, 88, (2025), 601-656.
14. Kusano, S. and Uchida, M.: Quasi-Akaike information criterion of SEM with latent variables for diffusion processes, Japanese Journal of Statistics and Data Science, 8, (2025), 217-264.
15. Tonaki, Y., Kaino, Y. and Uchida, M.: Small dispersion asymptotics for an SPDE in two space dimensions using triple increments, Journal of Statistical Planning and Inference, 241 (2026), 106333.

The Mathematical Society of Japan, The Japan Statistical Society, Japanese Society of Computational Statistics, International Statistical Institute.

Elected member of ISI (International Statistical Institute) (2012-)

Japanese Journal of Statistics and Data Science, coordinating editor (2017-)

The 18th JSS Ogawa Award, The Japan Statistical Society (2004)

The 7th JSS Research Award, The Japan Statistical Society (2013)

The 26th JJSS Award, The Japan Statistical Society (2021)