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An algorithm to fit regression models aimed at predicted the average responses beyond a conditional quantile level is presented. This procedure is implemented in a case study of insured drivers covering almost 10,000. The aim is to predict the expected yearly distance driven above the posted speed limits as a function of driving patterns such as total distance, urban and night percent driven. Gender and age are also controlled. Results are analyzed for the median and the top decile. The conclusions provide evidence of factors influencing speed limit violations for risky drivers and they are interesting to price motor insurance and implement road safety policies. The efficiency of the algorithm to fit tail expectation regression is compared to quantile regression. Computational time doubles for tail expectation regression compared to quantile regression. Standard errors are estimated via bootstrap methods. Further considerations regarding in-sample predictive performance are discussed. In particular, further restrictions should be imposed in the model specification to avoid prediction outside the plausible range.

An algorithm to fit conditional tail expectation regression models for vehicle excess speed in driving data