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Basics of Multivariate Analysis in Neuroimaging Data
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From multivariate to functional data analysis: fundamentals, recent developments, and emerging areas.

Yehua Li1, Yumou Qiu2, Yuhang Xu3

  • 1University of California - Riverside, Riverside, CA 92521, USA.

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|July 23, 2024
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Summary
This summary is machine-generated.

Functional data analysis (FDA) models infinite-dimensional data. This review covers FDA

Keywords:
Functional data analysisHigh-dimensional statisticsMulti-level modelingSpatial dependence

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Area of Science:

  • Statistics
  • Multivariate Analysis
  • Functional Data Analysis

Background:

  • Functional data analysis (FDA) is a statistical field for modeling infinite-dimensional random vectors.
  • It has gained prominence in the Journal of Multivariate Analysis.
  • Understanding FDA's origins and connections to multivariate analysis is crucial.

Purpose of the Study:

  • To review fundamental concepts of functional data analysis.
  • To explore recent advancements in FDA, including multi-level, high-dimensional, and dependent functional data.
  • To discuss the impact of these developments across various scientific and business domains.

Main Methods:

  • Review of fundamental concepts in functional data analysis.
  • Exploration of recent developments: multi-level FDA, high-dimensional functional regression, dependent functional data analysis.
  • Discussion of applications with real data examples.

Main Results:

  • Functional data analysis offers advanced methods for complex data.
  • Recent developments extend FDA to multi-level, high-dimensional, and dependent data structures.
  • FDA methodologies have significant impact on diverse fields like genetics and wearable device data.

Conclusions:

  • Functional data analysis is a rapidly evolving statistical discipline.
  • New methodologies are expanding the scope and applicability of FDA.
  • FDA provides powerful tools for analyzing complex data in science and industry.