Kernel Density Estimation for Actuarial Applications
Learn kernel density estimation techniques and their applications in actuarial loss modeling.
KDE Fundamentals
Kernel density estimation (KDE) provides a smooth nonparametric estimate of a probability density function. The estimator places a kernel function (typically Gaussian) centered at each data point and averages them. The bandwidth parameter h controls smoothness: larger h produces smoother estimates, while smaller h captures more local detail. The KDE at point x is f_hat(x) = (1/nh) times the sum of K((x - x_i)/h) over all observations. Bandwidth selection is critical and can use methods like cross-validation or Silverman's rule of thumb.
Actuarial Applications
In actuarial work, KDE is useful for visualizing loss distributions, comparing fitted parametric models to data, and estimating densities when no parametric family fits well. KDE can reveal multimodality, skewness, and other features that guide model selection. For Exam STAM, focus on understanding how bandwidth affects the estimate, computing KDE values at specific points using common kernels (uniform, triangular, Gaussian), and interpreting the resulting density estimates in the context of insurance loss modeling.