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A Parametric Bayesian Approach in Density Ratio Estimation

Author

Listed:
  • Abdolnasser Sadeghkhani

    (Department of Mathematics & Statistics, Brock University, St. Catharines, ON L2S 3A1, Canada)

  • Yingwei Peng

    (Departments of Public Health Sciences, Queen’s University, Kingston, ON K7L 3N6, Canada)

  • Chunfang Devon Lin

    (Department of Mathematics & Statistics, Queen’s University, Kingston, ON K7L 3N6, Canada)

Abstract

This paper is concerned with estimating the ratio of two distributions with different parameters and common supports. We consider a Bayesian approach based on the log–Huber loss function, which is resistant to outliers and useful for finding robust M-estimators. We propose two different types of Bayesian density ratio estimators and compare their performance in terms of frequentist risk function. Some applications, such as classification and divergence function estimation, are addressed.

Suggested Citation

  • Abdolnasser Sadeghkhani & Yingwei Peng & Chunfang Devon Lin, 2019. "A Parametric Bayesian Approach in Density Ratio Estimation," Stats, MDPI, vol. 2(2), pages 1-13, March.
    • Handle: RePEc:gam:jstats:v:2:y:2019:i:2:p:14-201:d:218593
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    References listed on IDEAS

    as
    1. Masashi Sugiyama & Taiji Suzuki & Shinichi Nakajima & Hisashi Kashima & Paul Bünau & Motoaki Kawanabe, 2008. "Direct importance estimation for covariate shift adaptation," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(4), pages 699-746, December.
    2. Krnjajic, Milovan & Kottas, Athanasios & Draper, David, 2008. "Parametric and nonparametric Bayesian model specification: A case study involving models for count data," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 2110-2128, January.
    3. Masashi Sugiyama & Taiji Suzuki & Takafumi Kanamori, 2012. "Density-ratio matching under the Bregman divergence: a unified framework of density-ratio estimation," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(5), pages 1009-1044, October.
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