A statistical test for the hypothesis of Gaussian random function

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

doi:10.1080/02331888.2018.1435659

A statistical test for the hypothesis of Gaussian random function

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

Department of Industrial and Systems Engineering

Research output: Contribution to journal › Article › peer-review

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
Pages (from-to)	801-817
Number of pages	17
Journal	Statistics
Volume	52
Issue number	4
DOIs	https://doi.org/10.1080/02331888.2018.1435659
Publication status	Published - 2018 Jul 4

Keywords

62F03
62F05
Normality test
asymptotic distribution
hypothesis test
random function

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1080/02331888.2018.1435659

Cite this

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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 = "62F03, 62F05, Normality test, asymptotic distribution, hypothesis test, random function",

author = "Shun Matsuura and Haruka Yamashita and Kinateder, {Kimberly K.J.}",

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A statistical test for the hypothesis of Gaussian random function

Abstract

Keywords

ASJC Scopus subject areas

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