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Density estimation for circular data observed with errors

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  • Marco Di Marzio
  • Stefania Fensore
  • Agnese Panzera
  • Charles C. Taylor

Abstract

Until now the problem of estimating circular densities when data are observed with errors has been mainly treated by Fourier series methods. We propose kernel‐based estimators exhibiting simple construction and easy implementation. Specifically, we consider three different approaches: the first one is based on the equivalence between kernel estimators using data corrupted with different levels of error. This proposal appears to be totally unexplored, despite its potential for application also in the Euclidean setting. The second approach relies on estimators whose weight functions are circular deconvolution kernels. Due to the periodicity of the involved densities, it requires ad hoc mathematical tools. Finally, the third one is based on the idea of correcting extra bias of kernel estimators which use contaminated data and is essentially an adaptation of the standard theory to the circular case. For all the proposed estimators, we derive asymptotic properties, provide some simulation results, and also discuss some possible generalizations and extensions. Real data case studies are also included.

Suggested Citation

  • Marco Di Marzio & Stefania Fensore & Agnese Panzera & Charles C. Taylor, 2022. "Density estimation for circular data observed with errors," Biometrics, The International Biometric Society, vol. 78(1), pages 248-260, March.
    • Handle: RePEc:bla:biomet:v:78:y:2022:i:1:p:248-260
    DOI: 10.1111/biom.13431
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    References listed on IDEAS

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    1. Johannes, Jan & Schwarz, Maik, 2013. "Adaptive circular deconvolution by model selection under unknown error distribution," LIDAM Reprints ISBA 2013048, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Di Marzio, Marco & Panzera, Agnese & Taylor, Charles C., 2009. "Local polynomial regression for circular predictors," Statistics & Probability Letters, Elsevier, vol. 79(19), pages 2066-2075, October.
    3. Raymond J. Carroll & Peter Hall, 2004. "Low order approximations in deconvolution and regression with errors in variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 31-46, February.
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