In the binary logistic regression model, a new type of estimator is proposed based on the first-order approximate modified ridge-type estimator method and the jackknife method. The sufficient conditions for the new estimator to be better than the first-order approximate modified ridge-type estimator and the first-order approximate maximum likelihood estimator under the criteria such as mean square error are discussed. At the same time, some of the theoretical results are illustrated by numerical simulation and empirical analysis. The results show that when the conditions in the theoretical results are met, the first-order approximate jackknifed ridge-type estimator is superior to the first-order approximate modified ridge-type estimator and first-order approximate maximum likelihood estimator under relevant criteria.
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