Nonparametric inference for discretely observed continuous-time and spatial processes

2019 Fiscal Year Final Research Report

• Project/Area Number: 19K20881
• Project/Area Number (Other): 18H05679 (2018)
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Multi-year Fund (2019); Single-year Grants (2018)
• Review Section: 0107:Economics, business administration, and related fields
• Research Institution: Tokyo Institute of Technology
• Principal Investigator: Kurisu Daisuke 東京工業大学, 工学院, 助教 (70825835)
• Project Period (FY): 2018-08-24 – 2020-03-31
• Keywords: レヴィ過程 / レヴィ駆動型確率過程 / 空間過程 / 経験過程 / ブートストラップ法

Outline of Final Research Achievements

In this project, the investigator worked on the following three studies.
①Nonparametric inference for Levy densities of Levy processes observed at high-frequency, ②Nonparametric inference for Levy measures of discretely observed Levy-driven stochastic processes, ③Nonparametric inference for mean and variance functions of nonparametric spatial regression models with irregularly spaced observations. Since the models studied in ①, ② are also important in engineering and physics as well as in finance and non-life insurance which are motivating examples in this project, the results can be applied to wide range of research fields. Moreover, I am planning to extend the results in ③ to more general framework such as spatio-temporal data so that we can consider spatial and temporal dependence simultaneously.

Free Research Field

数理統計学

Academic Significance and Societal Importance of the Research Achievements

研究①、②の成果により、金融機関等における実務家は理論的な妥当性を持つ統計手法を用いて金融商品や保険商品の将来のリスクを定量的に評価することが可能になる。研究③の成果により地価や気温、降水量などの空間的な従属構造を持つデータに対して設定される統計モデルに対してより正確な推定可能になる。さらに時間・空間的な従属性をもつより複雑かつ現実的な構造をもつデータに対する統計手法の理論解析への発展が期待される。