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PEBBLE: A second order correct bootstrap method in logistic regression
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DOI：10.3150/24-BEJ1827.png)
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Abstract
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Logistic regression is often used in many different fields, such as clinical trials, biomedical surveys, marketing, and banking, to predict the probability of a binary outcome. In this paper we propose a novel Bootstrap technique for approximating the distribution of the maximum likelihood estimator (MLE) of the regression parameter vector. Improved inference performance is obtained over the traditional normal approximation via establishing second order correctness. The main challenge in establishing second order correctness remains in the fact that the response variable being binary, the MLE may have a lattice structure resulting in non-existence of formal Edgeworth expansion. In order to achieve the second order correctness, a smoothing technique developed in Lahiri (J. Multivariate Anal. 45 (1993) 247-256) is adopted to define the original and Bootstrapped studentized pivots. Second order results are also extended to the one-dimensional smooth functions of the regression parameter e.g., odds ratio and success probability. Simulation experiments are performed to evaluate the finite-sample properties of the proposed Bootstrap method. The proposed methodology is demonstrated with an application on real dataset in healthcare operations.
Keywords:
Lattice
logistic regression
perturbation Bootstrap
smoothing
SOC
Journal
B
IF:
1.7
Papers:
106
Citations:
0
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