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A proportional likelihood ratio model

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  • Xiaodong Luo
  • Wei Yann Tsai

Abstract

We propose a semiparametric proportional likelihood ratio model which is particularly suitable for modelling a nonlinear monotonic relationship between the outcome variable and a covariate. This model extends the generalized linear model by leaving the distribution unspecified, and has a strong connection with semiparametric models such as the selection bias model (Gilbert et al., 1999), the density ratio model (Qin, 1998; Fokianos & Kaimi, 2006), the single-index model (Ichimura, 1993) and the exponential tilt regression model (Rathouz & Gao, 2009). A maximum likelihood estimator is obtained for the new model and its asymptotic properties are derived. An example and simulation study illustrate the use of the model. Copyright 2012, Oxford University Press.

Suggested Citation

  • Xiaodong Luo & Wei Yann Tsai, 2012. "A proportional likelihood ratio model," Biometrika, Biometrika Trust, vol. 99(1), pages 211-222.
    • Handle: RePEc:oup:biomet:v:99:y:2012:i:1:p:211-222
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    File URL: http://hdl.handle.net/10.1093/biomet/asr060
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    Cited by:

    1. Weibin Zhong & Guoqing Diao, 2023. "Joint semiparametric models for case‐cohort designs," Biometrics, The International Biometric Society, vol. 79(3), pages 1959-1971, September.
    2. Weibin Zhong & Guoqing Diao, 2023. "Semiparametric Density Ratio Model for Survival Data with a Cure Fraction," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 15(1), pages 217-241, April.
    3. Bhaskar Bhattacharya & Mohammad Al-talib, 2017. "A minimum relative entropy based correlation model between the response and covariates," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(4), pages 1095-1118, September.
    4. Archer Gong Zhang & Jiahua Chen, 2023. "Optimal Estimation under a Semiparametric Density Ratio Model," Papers 2309.09103, arXiv.org.
    5. Marchese, Scott & Diao, Guoqing, 2017. "Density ratio model for multivariate outcomes," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 249-261.
    6. Maria Gheorghe & Susan Picavet & Monique Verschuren & Werner B. F. Brouwer & Pieter H. M. Baal, 2017. "Health losses at the end of life: a Bayesian mixed beta regression approach," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(3), pages 723-749, June.
    7. Dörnemann, Nina, 2023. "Likelihood ratio tests under model misspecification in high dimensions," Journal of Multivariate Analysis, Elsevier, vol. 193(C).

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