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This study introduces a novel penalized quantile regression method for analyzing complex data with functional and scalar predictors. The approach enhances computational efficiency and variable selection for heavy-tailed skewed responses.

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Area of Science:

  • Statistics
  • Data Analysis
  • Biostatistics

Background:

  • Data analysis often involves heavy-tailed skewed responses linked to functional and scalar predictors.
  • Existing methods struggle with smoothness and computational efficiency in such scenarios.

Purpose of the Study:

  • To propose a new partially functional penalized convolution-type smoothed quantile regression model.
  • To enhance the characterization of conditional quantiles for scalar responses with mixed predictor types.
  • To improve computational efficiency and variable selection capabilities.

Main Methods:

  • Utilized a folded concave penalized estimator with a modified local adaptive majorize-minimization (LAMM) algorithm.
  • Approximated functional predictors using principal component basis for dense or sparse data.
  • Investigated consistency and oracle properties of the proposed estimators.

Main Results:

  • The new approach overcomes limitations of standard quantile empirical loss, improving computing efficiency.
  • Demonstrated competitive performance against standard partially functional penalized quantile regression via simulations.
  • Successfully applied the model to Alzheimer's Disease Neuroimaging Initiative data.

Conclusions:

  • The proposed penalized quantile regression offers a practical and efficient solution for analyzing complex datasets.
  • The method provides robust variable selection and estimation for functional and scalar covariates.
  • It holds significant potential for applications in fields like neuroimaging and other data-intensive research areas.