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Density estimation in the two-sample problem with likelihood ratio ordering

Author

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  • Tao Yu
  • Pengfei Li
  • Jing Qin

Abstract

SUMMARY In this paper, we propose a method for estimating the probability density functions in a two-sample problem where the ratio of the densities is monotone. This problem has been widely identified in the literature, but effective solution methods, in which the estimates should be probability densities and the corresponding density ratio should inherit monotonicity, are unavailable. If these conditions are not satisfied, the applications of the resultant density estimates might be limited. We propose estimates for which the ratio inherits the monotonicity property, and we explore their theoretical properties. One implication is that the corresponding receiver operating characteristic curve estimate is concave. Through numerical studies, we observe that both the density estimates and the receiver operating characteristic curve estimate from our method outperform those resulting directly from kernel density estimates, particularly when the sample size is relatively small.

Suggested Citation

  • Tao Yu & Pengfei Li & Jing Qin, 2017. "Density estimation in the two-sample problem with likelihood ratio ordering," Biometrika, Biometrika Trust, vol. 104(1), pages 141-152.
    • Handle: RePEc:oup:biomet:v:104:y:2017:i:1:p:141-152.
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    File URL: http://hdl.handle.net/10.1093/biomet/asw069
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    Cited by:

    1. Sangita Kulathinal & Isha Dewan, 2023. "Weighted U-statistics for likelihood-ratio ordering of bivariate data," Statistical Papers, Springer, vol. 64(2), pages 705-735, April.

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