Local Transformation Kernel Density Estimation of Loss Distributions

Abstract

We develop a tailor-made semiparametric asymmetric kernel density estimator for the estimation of actuarial loss distributions. The estimator is obtained by transforming the data with the generalized Champernowne distribution initially fitted to the data. Then the density of the transformed data is estimated by use of local asymmetric kernel methods to obtain superior estimation properties in the tails. We find in a vast simulation study that the proposed semiparametric estimation procedure performs well relative to alternative estimators. An application to operational loss data illustrates the proposed method.

KEY WORDS::

• Actuarial loss models
• Asymmetric kernels
• Champernowne distribution
• Local likelihood estimation
• Transformation