Nonparametric estimation for derivatives of compound distribution

The compound random variable ∑j=1NXj and its distribution have many applications in actuarial science. In this paper, we consider estimation of the derivative functionals of the compound distribution when the underlying density ff of XjXj is unknown. The estimator is constructed by Fourier inversion and kernel method. An order bound for the bias and asymptotic expression for the variance are given, and the asymptotic normality and uniform consistency are also discussed. Some simulation studies are presented to illustrate the performance of the estimator under finite sample setting.