vaikutuskäyrä

Vaikutuskäyrä, often translated as influence curve or influence function, is a statistical concept used to understand the effect of a single data point on a statistical estimate. It quantifies how much an estimator changes when a small amount of contamination is added to the data at a particular point. In simpler terms, it helps identify which data points are most influential in determining the outcome of a statistical calculation.

The influence function is a function that maps a data point to a value representing its impact. A large positive value for the influence function at a specific data point suggests that adding a small perturbation to that point will significantly increase the estimate. Conversely, a large negative value indicates that a perturbation will decrease the estimate. A value close to zero suggests the data point has little influence.

This concept is particularly important in robust statistics, where the goal is to develop methods that are not overly sensitive to outliers or unusual data points. By analyzing the influence curve, statisticians can assess the robustness of an estimator. Estimators with bounded influence curves are considered more robust, as the effect of any single data point is limited. It provides a theoretical tool for understanding the local behavior of estimators and is closely related to concepts like breakdown point.