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Significance tests for functional data with complex dependence structure.

Ana-Maria Staicu1, Soumen N Lahiri1, Raymond J Carroll2

  • 1Department of Statistics, North Carolina State University, United States.

Journal of Statistical Planning and Inference
|May 30, 2015
PubMed
Summary
This summary is machine-generated.

This study introduces a new statistical test for comparing multiple group mean functions in complex functional data. The method addresses multilevel and spatial structures, offering a novel approach for hypothesis testing.

Keywords:
Block bootstrapFunctional dataGroup mean testingHierarchical modelingSignificance testsSpatially correlated curves

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Area of Science:

  • Statistics
  • Functional Data Analysis
  • Multivariate Statistics

Background:

  • Functional data analysis often involves complex dependence structures.
  • Hypothesis testing for group mean functions is crucial in various scientific fields.
  • Existing methods may not adequately address multilevel and spatial correlations in functional data.

Purpose of the Study:

  • To develop a novel L2-norm based global testing procedure for comparing multiple group mean functions.
  • To address functional data with complex multilevel (groups-clusters/subjects-units) and spatial dependence structures.
  • To provide a statistically rigorous method for hypothesis testing in such intricate data settings.

Main Methods:

  • Utilizing orthogonal series expansions to approximate group mean functions.
  • Estimating the test statistic using basis coefficients derived from the data.
  • Developing the asymptotic null distribution of the test statistic under mild regularity conditions.
  • Proposing two small-sample alternatives, including a novel block bootstrap method for functional data.

Main Results:

  • The proposed L2-norm based test statistic is asymptotically valid under complex functional data structures.
  • Simulation studies demonstrate the performance of the proposed test and its small-sample alternatives.
  • This work represents the first study to address hypothesis testing for multilevel functional and spatial data.

Conclusions:

  • The developed testing procedure is effective for functional data with complex multilevel and spatial dependencies.
  • The proposed block bootstrap offers a viable alternative for small sample sizes.
  • The methodology is illustrated with a motivating real-world experiment.