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Minimum Rényi pseudodistance estimators for logistic regression models. (English) Zbl 1497.62195

Balakrishnan, Narayanaswamy (ed.) et al., Trends in mathematical, information and data sciences. A tribute to Leandro Pardo. Based on the presentations at the symposium on information theory with applications to statistical inference, Madrid, Spain, December 2, 2019. Cham: Springer. Stud. Syst. Decis. Control 445, 131-145 (2023).
Summary: In this work we propose a new family of estimators, called minimum Rényi pseudodistance estimators (MRPE), as a robust generalization of maximum likelihood estimators (MLE) for the logistic regression model based on the Rényi pseudodistance introduced by M. C. Jones et al. [Biometrika 88, No. 3, 865–873 (2001; Zbl 1180.62047)], along with their corresponding asymptotic distribution. Based on this information, we further develop three types of confidence intervals (approximate and parametric and non-parametric bootstrap ones). Finally, a simulation study is conducted considering different levels of outliers, where a better behavior of the MRPE with respect to the MLE is shown.
For the entire collection see [Zbl 1494.62008].

MSC:

62J12 Generalized linear models (logistic models)
62F35 Robustness and adaptive procedures (parametric inference)
62E20 Asymptotic distribution theory in statistics
62F25 Parametric tolerance and confidence regions
62F40 Bootstrap, jackknife and other resampling methods
62G09 Nonparametric statistical resampling methods

Citations:

Zbl 1180.62047
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References:

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