Frank Hampel

Frank Hampel (1941-2018) was a Swiss statistician who, alongside Peter Huber, established the theoretical foundations of robust statistics. His most influential contribution was the introduction of the breakdown point and the influence function as formal measures of estimator robustness, providing the conceptual tools that transformed robust statistics from a collection of ad hoc techniques into a rigorous mathematical discipline.

The Breakdown Point and Influence Function

Hampel's 1971 paper introduced the breakdown point: the proportion of contamination an estimator can tolerate before producing arbitrarily large errors. This simple concept had profound implications. It revealed that the sample mean, the most common estimator in statistics, has a breakdown point of zero percent — a single arbitrarily large outlier destroys it. The median, by contrast, has a breakdown point of fifty percent.

The influence function, also introduced by Hampel, provided a local measure of robustness: how much does a single infinitesimal contamination at a given point affect the estimator? Together, the breakdown point and influence function gave statisticians a dual framework for assessing robustness: global tolerance and local sensitivity.

Philosophy of Statistics

Hampel's work was driven by a conviction that statistical methods must be honest about their own fragility. He criticized the field's reliance on the normal distribution not because the normal distribution was wrong, but because methods optimized for it concealed their vulnerability. His robust statistics framework made that vulnerability explicit and measurable.