Abstract
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.
Highlights
IntroductionOur motivation for this paper is to adjust the risk level of drivers using car insurance telematics data
Interpolation of Quantile RegressionOur motivation for this paper is to adjust the risk level of drivers using car insurance telematics data
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
Summary
Our motivation for this paper is to adjust the risk level of drivers using car insurance telematics data. If all drivers had identical characteristics, direct one-to-one comparisons could be sufficient to identify dangerous individuals, but since drivers are not completely identical and they operate in a variety of circumstances, additional covariate information needs to be considered when assessing their risk. Quantile regression (Koenker and Bassett 1978) is a suitable method for finding conditional risk scores and it is a good instrument for our purposes (Pérez-Marín et al 2019; Guillen et al 2020). A driver’s risk score is defined as the quantile level at which the estimated conditional quantile is equal to the observed response. In order to fit a risk score to each driver, many quantile regressions need to be estimated. Some algorithms that suggest to obtain parameter estimates with one-step approximations may not be reliable for extreme quantile levels (Chernozhukov et al 2020)
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