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 languageEnglish
Pages (from-to)801-817
Number of pages17
JournalStatistics
Volume52
Issue number4
DOIs
Publication statusPublished - 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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