Improvement of nonparametric inference which has smoothness and higher order efficiency

2014 Fiscal Year Final Research Report

• Project/Area Number: 24650151
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Statistical science
• Research Institution: Kyushu University
• Principal Investigator: MAESONO Yoshihiko 九州大学, 数理(科)学研究科(研究院), 教授 (30173701)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: ノンパラメトリック / 順位検定 / カーネル型推定量 / 符号検定 / 正規近似 / 高次漸近理論 / ウィルコクソン検定 / エッジワース展開

Outline of Final Research Achievements

In this project, we propose smoothed rank tests based on the kernel method which gives us smooth statistical inference. The proposed tests conquer the problem of the discreteness of the distribution for rank tests. We also obtain theoretical properties of the smoothed rank tests, and show the proposed tests are asymptotically equivalent to the ordinary rank tests. Further we obtain Edgeworth expansions of these tests, which are improvements of the normal approximations. If we choose proper kernels, we can get the Edgewroth expansions which do not depend on the population distribution. These results are unique and forefront of this area.

Free Research Field

統計科学