Nonparametric Estimation of Splicing Points in Actuarial Loss Distributions via Data Transformation

We propose a nonparametric method for estimating splicing points in actuarial loss distributions. Our approach transforms non-negative loss data onto the unit interval [0,1] via the transformation based on the cumulative distribution function of the log–logistic (or Fisk) distribution, which magnifies jump discontinuities in the density and facilitates detection of the splicing point even in the sparse tail region. The transformed data are smoothed using the asymmetric beta kernel, and the splicing point estimator is obtained by back-transforming the maximizer of a diagnostic function. It is demonstrated that the proposed splicing point estimator is strongly consistent and asymptotically normal with a convergence rate faster than the parametric one. Monte Carlo simulations and applications to non-life insurance loss data confirm the practical relevance of the approach.