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Joint Estimation of the Mean and Error Distribution in Generalized Linear Models

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  • Alan Huang

Abstract

This article introduces a semiparametric extension of generalized linear models that is based on a full probability model, but does not require specification of an error distribution or variance function for the data. The approach involves treating the error distribution as an infinite-dimensional parameter, which is then estimated simultaneously with the mean-model parameters using a maximum empirical likelihood approach. The resulting estimators are shown to be consistent and jointly asymptotically normal in distribution. When interest lies only in inferences on the mean-model parameters, we show that maximizing out the error distribution leads to profile empirical log-likelihood ratio statistics that have asymptotic χ-super-2 distributions under the null. Simulation studies demonstrate that the proposed method can be more accurate than existing methods that offer the same level of flexibility and generality, especially with smaller sample sizes. The theoretical and numerical results are complemented by a data analysis example. Supplementary materials for this article are available online.

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  • Alan Huang, 2014. "Joint Estimation of the Mean and Error Distribution in Generalized Linear Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 186-196, March.
    • Handle: RePEc:taf:jnlasa:v:109:y:2014:i:505:p:186-196
    DOI: 10.1080/01621459.2013.824892
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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. Marchese, Scott & Diao, Guoqing, 2017. "Density ratio model for multivariate outcomes," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 249-261.
    4. Marchese, Scott & Diao, Guoqing, 2018. "Joint regression analysis of mixed-type outcome data via efficient scores," Computational Statistics & Data Analysis, Elsevier, vol. 125(C), pages 156-170.

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