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Density estimation and regression analysis on hyperspheres in the presence of measurement error

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  • Jeong Min Jeon
  • Ingrid Van Keilegom

Abstract

This paper studies density estimation and regression analysis with data observed on a general unit hypersphere and contaminated by measurement errors. We establish novel density and regression estimators, and study their asymptotic properties such as the rates of convergence and asymptotic normality. We also provide two types of asymptotic confidence intervals for both density and regression functions. One type is based on the asymptotic normality of their estimators and the other type is based on the empirical likelihood technique. We present practical details on the implementation of our method as well as simulation studies and real data analysis.

Suggested Citation

  • Jeong Min Jeon & Ingrid Van Keilegom, 2024. "Density estimation and regression analysis on hyperspheres in the presence of measurement error," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 51(2), pages 513-556, June.
    • Handle: RePEc:bla:scjsta:v:51:y:2024:i:2:p:513-556
    DOI: 10.1111/sjos.12684
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    References listed on IDEAS

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