Dependence properties and estimation of B-spline copulas

2019 Fiscal Year Final Research Report

• 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
• 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

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.

Free Research Field

統計科学

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.