BoundaryBias

Boundary bias refers to a systematic distortion in estimators or predictive models that occurs near the edges of the input domain or close to decision boundaries. It arises when data are sparse at the boundary, or when estimation methods assume the existence of data beyond the boundary, leading to distorted estimates or predictions.

In kernel density estimation and nonparametric regression, boundary bias is well known. On a finite support, kernels extend beyond the domain, causing the mass near the boundary to be misrepresented and leading to underestimated density or biased regression function values. Mitigation approaches include boundary corrections such as data reflection, boundary-corrected kernels, or the use of local polynomial regression that reduces edge bias.

In classification, boundary bias affects the estimated decision boundary or posterior probabilities, particularly under class imbalance or sampling bias, which can cause misclassification near the edge of class regions. It can also influence the calibration of predicted probabilities.

Mitigation strategies commonly involve boundary correction techniques, data augmentation near edges, and transformations that map bounded domains to the real line (for example, logit or probit transforms). Other approaches include using asymmetric or boundary-aware kernels, adaptive bandwidth selection, higher-order local polynomials, or estimators designed specifically for bounded domains.

Boundary bias is related to edge effects and sampling bias, and understanding its presence is important for assessing the reliability of estimates and predictions near domain boundaries.