# A statistical test for the hypothesis of Gaussian random function

Shun Matsuura, Haruka Yamashita, Kimberly K.J. Kinateder

Research output: Contribution to journalArticle

### Abstract

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.

Original language English 1-17 17 Statistics https://doi.org/10.1080/02331888.2018.1435659 Accepted/In press - 2018 Feb 14

### Fingerprint

Gaussian Function
Random Function
Statistical test
Asymptotic Power
Unbiased estimator
Hypothesis Test
Asymptotic distribution
Test Statistic
Gaussian distribution
Estimator
Numerical Simulation
Statistical tests

### Keywords

• asymptotic distribution
• hypothesis test
• Normality test
• random function

### ASJC Scopus subject areas

• Statistics and Probability
• Statistics, Probability and Uncertainty

### Cite this

A statistical test for the hypothesis of Gaussian random function. / Matsuura, Shun; Yamashita, Haruka; Kinateder, Kimberly K.J.

In: Statistics, 14.02.2018, p. 1-17.

Research output: Contribution to journalArticle

Matsuura, Shun ; Yamashita, Haruka ; Kinateder, Kimberly K.J. / A statistical test for the hypothesis of Gaussian random function. In: Statistics. 2018 ; pp. 1-17.
title = "A statistical test for the hypothesis of Gaussian random function",
abstract = "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.",
keywords = "asymptotic distribution, hypothesis test, Normality test, random function",
author = "Shun Matsuura and Haruka Yamashita and Kinateder, {Kimberly K.J.}",
year = "2018",
month = "2",
day = "14",
doi = "10.1080/02331888.2018.1435659",
language = "English",
pages = "1--17",
journal = "Statistics",
issn = "0233-1888",
publisher = "Taylor and Francis Ltd.",

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AU - Matsuura, Shun

AU - Yamashita, Haruka

AU - Kinateder, Kimberly K.J.

PY - 2018/2/14

Y1 - 2018/2/14

N2 - 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.

AB - 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.

KW - asymptotic distribution

KW - hypothesis test

KW - Normality test

KW - random function

UR - http://www.scopus.com/inward/record.url?scp=85042215159&partnerID=8YFLogxK

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JF - Statistics

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