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This study introduces robust M-estimators for analyzing irregular functional data, improving modeling and inference for applications like quantitative ultrasound. The methods provide reliable statistical analysis even with incomplete or outlier data.

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Area of Science:

  • Statistics
  • Functional Data Analysis
  • Quantitative Ultrasound

Background:

  • Irregularly sampled functional data presents modeling challenges.
  • Outlier curves can significantly impact statistical inference.
  • Quantitative ultrasound (QUS) analysis involves complex, often irregular, signal data.

Purpose of the Study:

  • To develop robust M-estimators for partially observed functional data.
  • To address sensitivity to outlier curves in functional data analysis.
  • To apply these methods to quantitative ultrasound signal analysis.

Main Methods:

  • Investigated a class of robust M-estimators, including functional location and quantile estimators.
  • Established consistency of estimators under general partial observation conditions.
  • Developed asymptotic Gaussian process approximations for large sample inference.

Main Results:

  • Demonstrated consistency of the proposed robust M-estimators.
  • Established asymptotic Gaussian process approximations for robust inference.
  • Validated the performance through simulations and real QUS data analysis.

Conclusions:

  • The proposed robust M-estimators are effective for partially observed functional data.
  • Asymptotic approximations and bootstrap methods provide reliable inference.
  • The methods offer a robust approach for quantitative ultrasound signal analysis.