高頻度時系列データに基づく確率微分方程式（SDE）の統計モデリングについて研究しています．具体的にはSDEモデルの統計的推定や仮説検定のための漸近理論の構築，およびモデル選択のための情報量規準の構成とその数学的正当化に取り組んでいます．さらに，高頻度時空間データを用いた確率偏微分方程式（SPDE）の統計的漸近理論についても研究しており，SPDEの係数パラメータ推測手法の開発とその理論的基盤の整備を進めています．また，高頻度時系列および時空間データ解析を用いた実証研究にも関心を持ち，理論と応用の両面から統計モデリングの発展を目指しています．

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.

21世紀の統計科学III. 東京大学出版会 2008 (共著)

統計学辞典. 共立出版 2010 (共訳)

第18回日本統計学会小川研究奨励賞 (2004)

第7回日本統計学会研究業績賞 (2013)

第26回日本統計学会賞 (2021)

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

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