Asymptotic Expansions for U- and V-statistics with Degenerate Kernels
| Project/Area Number |
25400211
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Foundations of mathematics/Applied mathematics
|
|---|
| Research Institution | Tokyo City University |
|---|
Principal Investigator |
Kanagawa Shuya 東京都市大学, 共通教育部, 教授 (50185899)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
前園 宜彦 九州大学, 数理学研究院, 教授 (30173701)
税所 康正 広島大学, 工学研究科, 准教授 (70195973)
|
|---|
| Project Period (FY) |
2013-04-01 – 2018-03-31
|
| Project Status |
Completed (Fiscal Year 2017)
|
| Budget Amount *help |
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
|
|---|
| Keywords | Symmetric Statistics / Central Limit Theorem / Asymptotic Expansion / U-statistics / V-statistics / Edgeworth expansion / 対称統計量 / 退化型対称統計量 / エッジワース展開 / Cramer-Von Mises統計量 / 従属確率変数列 / 混合性 / 漸近展開 / U-統計量 / V-統計量 / 中心極限定理 / ヒルベルト空間値確率変数 / 対称統計量の漸近理論 / 時系列モデル / 数理ファイナンス / ボラティリティ推定 / 確率微分方程式 / オイラー・丸山近似 / 従属確率変数 / 変化点解析 / 拡散過程 / 複合ポアソン過程 / 時系列データ / 非線形シュレディンガー方程式 / 信頼区間 |
|---|
| Outline of Final Research Achievements |
We consider asymptotically normal statistics which are symmetric functions of N i.i.d. random variables. For these statistics we prove the va- lidity of an Edgeworth expansion with remainder of the large order of n to the power of (-2) under Cramer’s condition on the linear part of the statistic and moment assumptions for all parts of the statistic. By means of a counterexample we show that it is generally not possible to obtain an Edgeworth expansion with remainder of the large order of n to the power of (-2) without imposing additional assumptions on the structure of the nonlinear part of the statistic.
|
Report
(6 results)
Research Products
(30 results)
