Multivariate statistical inference for high-dimensional data and its application

2017 Fiscal Year Final Research Report

• Project/Area Number: 26800088
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Kagoshima University (2016-2017); Nihon University (2014-2015)
• Principal Investigator: YAMADA Takayuki 鹿児島大学, 共通教育センター, 講師 (60510956)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: 多変量解析 / 高次元データ / 漸近理論

Outline of Final Research Achievements

Firstly, we propose an estimate of multivariate 3rd moment which is well defined for the case that the dimensionality of the observation vector is larger than the sample size. As an application, we apply to testing the multivariate normality.

Secondary, we propose a cut-off point for the classical linear discriminant rule in 2 groups which one of two types of expected probability of misclassification takes pre-setting level. It is derived by the asymptotic distribution for the studentized linear discriminant function under the assumption that the population has multivariate normal distribution. The asymptotic distribution which we dealt is under the high-dimensional asymptotic framework that the dimension and the sample size go to infinity together while the ratio of the dimension to the sample size converges to a constant in [0,1).

Free Research Field

数理統計学