A statistical test for the hypothesis of Gaussian random function

被引：0
|
作者：
Matsuura, Shun [1 ]
Yamashita, Haruka [2 ]
Kinateder, Kimberly K. J. [3 ]
机构：
[1] Keio Univ, Fac Sci & Technol, Yokohama, Kanagawa, Japan
[2] Sophia Univ, Fac Sci & Technol, Tokyo, Japan
[3] Wright State Univ, Dept Math & Stat, Dayton, OH 45435 USA
来源：
STATISTICS | 2018年 / 52卷 / 04期
基金：
日本学术振兴会;
关键词：
Normality test; random function; hypothesis test; asymptotic distribution; MULTIVARIATE NORMALITY; MATRIX;
D O I：
10.1080/02331888.2018.1435659
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
A Gaussian random function is a functional version of the normal distribution. This paper proposes a statistical hypothesis test to test whether or not a random function is a Gaussian random function. A parameter that is equal to 0 under Gaussian random function is considered, and its unbiased estimator is given. The asymptotic distribution of the estimator is studied, which is used for constructing a test statistic and discussing its asymptotic power. The performance of the proposed test is investigated through several numerical simulations. An illustrative example is also presented.
引用
收藏
页码：801 / 817
页数：17
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