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  • 1Department of Statistics, North Carolina State University, Raleigh, NC 27695-8203, USA.

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Summary
This summary is machine-generated.

We developed covariate-adjusted skewed functional models (cSFM) for analyzing functional data with location-dependent distributions. This method enables accurate quantile estimation and trajectory prediction, even with sparse data.

Keywords:
Covariate modelingDiffusion tensor imagingFunctional principal component analysisGaussian copulaQuantile estimationSkewed function

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Area of Science:

  • Statistics
  • Functional Data Analysis
  • Biostatistics

Background:

  • Functional data analysis often encounters challenges with location-dependent marginal distributions.
  • Existing models may not adequately capture complex dependencies in such data.

Purpose of the Study:

  • To introduce a novel class of covariate-adjusted skewed functional models (cSFM).
  • To provide a unified framework for pointwise quantile estimation and trajectory prediction in functional data analysis.
  • To develop a computationally feasible method for both dense and sparse functional data.

Main Methods:

  • A semi-parametric copula model is proposed for pointwise marginal distributions dependent on covariates.
  • Functional dependence is modeled as covariate-invariant.
  • The framework handles densely and sparsely observed functional data.

Main Results:

  • The proposed cSFM framework offers a unifying approach for quantile estimation and trajectory prediction.
  • The methodology is computationally feasible for various data observation densities.
  • Simulations demonstrate the effectiveness of the methods.

Conclusions:

  • The covariate-adjusted skewed functional models (cSFM) provide a flexible and powerful tool for analyzing functional data with complex marginal distributions.
  • The R package cSFM is available for practical implementation.
  • The method was successfully applied to a tractography study in multiple sclerosis.