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Density estimation for circular data observed with errors.

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Quasi-likelihood estimation for semiparametric circular regression models.

Anna Gottard1, Andrea Meilán-Vila2, Agnese Panzera1

  • 1Department of Statistics, Computer Science, Applications, University of Florence, 50134 Florence, Italy.

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|February 3, 2026
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Summary
This summary is machine-generated.

This study introduces a flexible semiparametric regression model for analyzing circular data, offering interpretable insights into genetic influences on animal migration patterns.

Keywords:
backfitting algorithmbird migration patternscircular datacircular quasi-likelihoodkernel smoothing

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Area of Science:

  • Statistics
  • Genetics
  • Ecology

Background:

  • Circular data analysis requires flexible and interpretable models.
  • Existing methods may lack adaptability for complex covariate structures.

Purpose of the Study:

  • To develop a semiparametric regression model for circular responses.
  • To accommodate both linear and circular covariates.
  • To provide a robust framework for analyzing biological data with circular characteristics.

Main Methods:

  • Developed a semiparametric regression model for circular data.
  • Employed a circular quasi-likelihood function, avoiding distributional assumptions.
  • Utilized a backfitting algorithm for model estimation.
  • Assessed model performance via simulations.

Main Results:

  • The proposed model demonstrates flexibility and interpretability.
  • The method effectively handles mixed linear and circular covariates.
  • Simulations confirm good finite-sample performance.

Conclusions:

  • The semiparametric model offers a valuable tool for circular data analysis.
  • It provides novel insights into the genetic basis of migratory behavior in willow warblers.
  • This approach enhances understanding of genomic influences on ecological phenomena.