From multivariate to functional data analysis: fundamentals, recent developments, and emerging areas

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.