Abstract
An expression of the mean squared error, MSE, of prediction for new observations when using logistic regression is showed. First, MSE is approximated by the sum of the process variance and of the estimation variance. The estimation variance can be estimated by applying the delta method and/or by using bootstrap methodology. When using bootstrap, e.g. bootstrap residuals, it is possible to obtain an estimation of the distribution for each predicted value. Confidence intervals can be calculated taking into account the bootstrapped distributions of the predicted new values to help us in the knowledge of their randomness. The general formulas of prediction error (the square root of MSE of prediction), PE, in the cases of the power family of error distributions and of the power family of link functions for generalized linear models were obtained in previous works. Now, the expression of the MSE of prediction for the generalized linear model with Binomial error distribution and logit link function, the logistic regression, is obtained. Its calculus and usefulness are illustrated with real data to solve the problem of Credit Scoring, where policyholders are classified into defaulters and non-defaulters.
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Spanish Ministry of Economy and Competitiveness, MTM2014-56535-R.
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Boj, E., Costa, T. (2018). Logistic Classification for New Policyholders Taking into Account Prediction Error. In: Corazza, M., Durbán, M., Grané, A., Perna, C., Sibillo, M. (eds) Mathematical and Statistical Methods for Actuarial Sciences and Finance. Springer, Cham. https://doi.org/10.1007/978-3-319-89824-7_30
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DOI: https://doi.org/10.1007/978-3-319-89824-7_30
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