Delong, Ł., Wüthrich, 2023, The role of the variance function in mean estimation and validation
Working Paper, 01-07-2023
Regression modeling for insurance pricing mostly focuses on mean estimation. Using a strictly consistent loss function implies that the mean estimates are asymptotically correct. However, this is a limiting statement and insurance prices are calculated on finite samples. It is known that under heteroskedasticity suitable variance estimates can significantly improve the regression model estimation. In this paper we investigate isotonic regression which is a nonparametric rank-preserving regression approach. This isotonic regression is used to (1) explore the power variance parameter of the variance function within Tweedie’s family of distributions, (2) derive a semi-parametric bootstrap under heteroskedasticity, (3) provide a test for autocalibration, (4) explore a quasi-likelihood approach to benefit from best-asymptotic estimation, (5) deal with several difficulties under lognormal assumptions. In all these problems we verify that variance estimation using an isotonic regression is very beneficial.