Robust Statistics: Handling Outliers in Insurance Data
Apply robust statistical methods to handle outliers and heavy-tailed insurance data for Exam MAS-I.
Why Robustness Matters
Insurance data frequently contains outliers from catastrophic claims, data errors, or heavy-tailed distributions. The sample mean has a breakdown point of 1/n (one extreme observation can make it arbitrarily large), making it highly sensitive to outliers. Robust statistics have high breakdown points and bounded influence functions. The breakdown point is the smallest fraction of contamination that can make the estimator arbitrarily bad. Robust location estimators include the median (50% breakdown), trimmed mean, and Winsorized mean. The median absolute deviation (MAD) provides robust scale estimation.
Robust Regression and Applications
Robust regression methods resist the influence of outlying observations. M-estimation generalizes MLE using a loss function less sensitive to extreme residuals (Huber's function uses squared loss near zero and absolute loss in the tails). Least trimmed squares fits regression to the h observations with smallest residuals. The influence function IF(x; T, F) measures the effect of a single observation on the estimator. In actuarial work, robust methods improve parameter estimation for loss distributions, credibility estimates, and regression-based pricing models when data quality varies. Exam MAS-I covers basic robustness concepts.