Interpolation of quantile regression to estimate driver's risk of traffic accident based on excess speed

Quantile regression provides a way to estimate a driver's risk of a traffic accident by means of predicting the percentile of observed distance driven above the legal speed limits over a one year time interval, conditional on some given characteristics such as total distance driven, age, gender, percent of urban zone driving and night time driving. This study proposes an approximation of quantile regression coefficients by interpolating only a few quantile levels, which can be chosen carefully from the unconditional empirical distribution function of the response. Choosing the levels before interpolation improves accuracy. This approximation method is convenient for real-time implementation of risky driving identification and provides a fast approximate calculation of a risk score. We illustrate our results with data on 9614 drivers observed over one year.