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Wavelet analysis of variance box plot.

Jeffrey Williams¹, Raymond R Hill¹, Joseph J Pignatiello¹

¹Air Force Institute of Technology, Wright-Patterson Air Force Base, Dayton, OH, USA.

Journal of Applied Statistics

|October 17, 2022

Summary

This summary is machine-generated.

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Functional box plots offer new ways to visualize and analyze functional data. Wavelet analysis of variance (WANOVA) box plots improve outlier detection, especially for shape outliers in noisy data.

Area of Science:

Statistics
Data Analysis
Functional Data Analysis

Background:

Traditional statistical methods often miss key characteristics of functional datasets.
Existing functional data analysis tools have limitations in outlier detection.

Purpose of the Study:

To introduce functional box plots for visualizing and statistically analyzing functional data.
To enhance outlier detection in functional data using wavelet analysis.

Main Methods:

Utilized a depth method for visualizing and ranking functional curves.
Integrated wavelet analysis as a mechanism for generating functional box plots.
Developed the wavelet analysis of variance (WANOVA) box plot tool.

Main Results:

Keywords:

Outliers box plots functional data functional data analysis wavelets

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Functional box plots provide novel comparisons suited for functional data.
WANOVA box plots demonstrate competitive error rates for magnitude outliers.
WANOVA box plots outperform traditional functional box plots for shape outlier detection in Gaussian data.

Conclusions:

Wavelet analysis is effective for approximating irregular and noisy functional data.
WANOVA box plots offer enhanced capabilities for classifying shape outliers in both simulated and real data.