A nonparametric sequential learning procedure for estimating the pure premium

With the advent of the “big” data era, large-sample properties of a statistical learning method are becoming more and more important in an actuary’s daily work. For a fixed sample size, regardless of how large it is, the variance of an estimator can be larger than a pre-assigned level to an arbitrary extent. In this paper, we propose a nonparametric sequential learning procedure for estimating the pure premium. Our method not only provides an accurate estimate of the pure premium but also guarantees that the mean of our random sample sizes is close to the unobservable optimal fixed sample size and the variance of our estimator is close to all small pre-determined levels. In addition, our method is nonparametric and applicable to any claims distribution; hence it avoids potential issues associated with a parametric model such as model misspecification risk and the effect of selection.