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Minimizing robust density power-based divergences for general parametric density models

Author

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  • Akifumi Okuno

    (Institute of Statistical Mathematics
    RIKEN Center for Advanced Intelligence Project)

Abstract

Density power divergence (DPD) is designed to robustly estimate the underlying distribution of observations, in the presence of outliers. However, DPD involves an integral of the power of the parametric density models to be estimated; the explicit form of the integral term can be derived only for specific densities, such as normal and exponential densities. While we may perform a numerical integration for each iteration of the optimization algorithms, the computational complexity has hindered the practical application of DPD-based estimation to more general parametric densities. To address the issue, this study introduces a stochastic approach to minimize DPD for general parametric density models. The proposed approach can also be employed to minimize other density power-based $$\gamma$$ γ -divergences, by leveraging unnormalized models. We provide R package for implementation of the proposed approach in https://github.com/oknakfm/sgdpd .

Suggested Citation

  • Akifumi Okuno, 2024. "Minimizing robust density power-based divergences for general parametric density models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 76(5), pages 851-875, October.
    • Handle: RePEc:spr:aistmt:v:76:y:2024:i:5:d:10.1007_s10463-024-00906-9
    DOI: 10.1007/s10463-024-00906-9
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    References listed on IDEAS

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    1. Hirose, Kei & Fujisawa, Hironori & Sese, Jun, 2017. "Robust sparse Gaussian graphical modeling," Journal of Multivariate Analysis, Elsevier, vol. 161(C), pages 172-190.
    2. Jack Jewson & David Rossell, 2022. "General Bayesian loss function selection and the use of improper models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(5), pages 1640-1665, November.
    3. Abhik Ghosh & Ayanendranath Basu, 2016. "Robust Bayes estimation using the density power divergence," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 68(2), pages 413-437, April.
    4. Fujisawa, Hironori & Eguchi, Shinto, 2008. "Robust parameter estimation with a small bias against heavy contamination," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 2053-2081, October.
    5. Takafumi Kanamori & Hironori Fujisawa, 2015. "Robust estimation under heavy contamination using unnormalized models," Biometrika, Biometrika Trust, vol. 102(3), pages 559-572.
    6. A. Philip Dawid & Monica Musio & Laura Ventura, 2016. "Minimum Scoring Rule Inference," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(1), pages 123-138, March.
    7. Amarnath Nandy & Ayanendranath Basu & Abhik Ghosh, 2022. "Robust inference for skewed data in health sciences," Journal of Applied Statistics, Taylor & Francis Journals, vol. 49(8), pages 2093-2123, June.
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