Parametric vs. Nonparametric Estimation for Exam STAM

Parametric Estimation

Parametric estimation assumes losses follow a specific distributional family (e.g., lognormal, Pareto, gamma) and estimates the parameters from data. Methods include maximum likelihood estimation (MLE) and method of moments. Parametric models provide smooth, complete distribution functions useful for extrapolation and pricing. However, if the assumed family is wrong, estimates can be significantly biased. MLE is preferred for Exam STAM because it handles censored and truncated data naturally through likelihood construction.

Nonparametric Estimation

Nonparametric methods make no distributional assumptions. The empirical distribution function assigns probability 1/n to each observation. The Kaplan-Meier estimator handles right-censored data, and the Nelson-Aalen estimator provides cumulative hazard estimates. These methods are flexible and robust but produce step functions that can be noisy with small samples. They cannot extrapolate beyond observed data. Exam STAM tests your ability to compute both types of estimates and to recognize when each approach is appropriate.