Dependence properties and estimation of B-spline copulas
Project/Area Number |
16K00060
|
Research Category |
Grant-in-Aid for Scientific Research (C)
|
Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Statistical science
|
Research Institution | Waseda University |
Principal Investigator |
DOU XIAOLING 早稲田大学, データ科学センター, 准教授(任期付) (10516868)
|
Project Period (FY) |
2016-04-01 – 2020-03-31
|
Project Status |
Completed (Fiscal Year 2019)
|
Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2018: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2017: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
|
Keywords | コピュラ / 多変量分布 / 分布の相関構造 / 分布の推定 / EMアルゴリズム / B-spline関数 / B-splineコピュラ / Baker分布 / Bernsteinコピュラ / Total positivity / 順序統計量 / モーメント / 相関係数 / 相関を最大にするコピュラ / 第二種のスターリン数 / B-spline基底関数 / 基底関数の次数 / 基底関数の数 / Bernstein関数 / 相関構造 / 推定方法 / 高次元 / スプライン関数 |
Outline of Final Research Achievements |
Based on B-spline basis functions, we define a new class of copulas, called B-spline copulas. The B-spline copulas include the Bernstein copulas as a special case where the basis functions are generated without interior knots. By comparing the ranges of the maximum correlation of the B-spline copulas and the Bernstein copulas, we found that the B-spline copulas are more flexible. That is, with less basis functions, they can express higher correlations. We showed that the B-spline copulas of the maximum correlation case can attain the Frechet Hoeffding upper bound when the number of basis functions goes to infinity. We also proved the B-spline copulas of the maximum correlation case have total positivity of any order. We proposed to estimate the B-spline copulas by a grid method and some EM algorithms. These methods are examined with real data sets.
|
Academic Significance and Societal Importance of the Research Achievements |
コピュラは金融工学やリスク, 土木工学等多くの分野で活用されている. 実際に様々なデータに対して, シミュレーションやモデリングするためには、柔軟性の高いコピュラが望ましい. B-splineコピュラを定義し, その相関構造の性質を調べることで, B-splineコピュラは従来のコピュラより高い柔軟性を持ち, 多様なデータ構造を表現することができることが分かった. また, 少ない基底関数で高い相関を表せることは計算コストも少なくなる. さらに, グリッド法やEMアルゴリズムの方法でB-splineコピュラを推定できるので, B-splineコピュラが幅広く利用できると思う.
|
Report
(5 results)
Research Products
(37 results)
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
[Presentation] B-spline copula and its estimation2016
Author(s)
Xiaoling Dou
Organizer
The 10th ICSA International Conference on Global Growth of Modern Statistics in the 21st Century
Place of Presentation
Shanghai Jiao Tong University
Year and Date
2016-12-19
Related Report
Int'l Joint Research / Invited
-
-