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

页码：801 / 817

页数：17

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