Nonparametric Estimation of the Laplace Transform from Empirical Data Using Symmetric Kernels Method

Focusing on the use of a Gaussian kernel, the paper constructs a nonparametric Laplace transform estimator via symmetric kernel methodology. Convergence rates and an asymptotic mean integrated squared error (AMISE) formula are used to establish theoretical properties of the estimator and guide optimal bandwidth choice. Finite-sample performance is evaluated through comprehensive simulations. Real and synthetic data applications illustrate practical utility. Estimator robustness and accuracy are showed in outcomes, interpretation the implement valuable across statistical and practical fields.