LR tests for two hypotheses in profile analysis of growth curve data

Takashi Seo, Tomoko Sakurai, Yasunori Fujikoshi

Research output: Contribution to journalArticle

3 Citations (Scopus)


This paper is concerned with profile analysis of k p-dimensional normal populations Πi: Npi, Σ), i = 1,·, k, when the mean vectors are expressed as μi = Xθi, i = 1, ·, k, where X is a p × q given matrix with rank q and θi's are unknown parameter vectors. The model with such a mean structure is applied to growth curve data. Fujikoshi (2009) studied a likelihood ratio statistic for a parallelism hypothesis. In this paper we derive likelihood ratio statistics for level and flatness hypotheses under the parallelism hypothesis. Their null distributions are obtained. We also give an example.

Original languageEnglish
Pages (from-to)105-118
Number of pages14
JournalSUT Journal of Mathematics
Issue number2
Publication statusPublished - 1 Dec 2011



  • Distributions of test statistics
  • Flatness hypothesis
  • Growth curve model
  • Level hypothesis
  • Likelihood ratio tests
  • Parallelism hypothesis

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