Likelihood ratio tests for dependent data with applications to longitudinal and functional data analysis

Ana Maria Staicu, Yingxing Li, Ciprian M Crainiceanu, David Ruppert

Research output: Contribution to journalArticle

Abstract

This paper introduces a general framework for testing hypotheses about the structure of the mean function of complex functional processes. Important particular cases of the proposed framework are as follows: (1) testing the null hypothesis that the mean of a functional process is parametric against a general alternative modelled by penalized splines; and (2) testing the null hypothesis that the means of two possibly correlated functional processes are equal or differ by only a simple parametric function. A global pseudo-likelihood ratio test is proposed, and its asymptotic distribution is derived. The size and power properties of the test are confirmed in realistic simulation scenarios. Finite-sample power results indicate that the proposed test is much more powerful than competing alternatives. Methods are applied to testing the equality between the means of normalized δ-power of sleep electroencephalograms of subjects with sleep-disordered breathing and matched controls.

Original languageEnglish (US)
Pages (from-to)932-949
Number of pages18
JournalScandinavian Journal of Statistics
Volume41
Issue number4
DOIs
StatePublished - Dec 1 2014

Fingerprint

Longitudinal Data Analysis
Functional Data Analysis
Dependent Data
Likelihood Ratio Test
Sleep
Null hypothesis
Testing
Penalized Splines
Pseudo-likelihood
Testing Hypotheses
Alternatives
Asymptotic distribution
Equality
Scenarios
Likelihood ratio test
Simulation
Framework

Keywords

  • Functional data
  • Longitudinal data
  • Pseudo-likelihood
  • Sleep health heart study
  • Two-sample problem

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Likelihood ratio tests for dependent data with applications to longitudinal and functional data analysis. / Staicu, Ana Maria; Li, Yingxing; Crainiceanu, Ciprian M; Ruppert, David.

In: Scandinavian Journal of Statistics, Vol. 41, No. 4, 01.12.2014, p. 932-949.

Research output: Contribution to journalArticle

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