biascorrected

Bias correction, or bias-corrected, refers to methods that adjust estimators to reduce systematic error, or bias. Bias is the difference between an estimator’s expected value and the true parameter. When bias arises from small samples, measurement error, or model misspecification, bias-corrected procedures aim to make estimates more accurate on average.

Analytical bias correction uses an estimated bias term and subtracts it from the estimator. Bootstrap bias correction relies on resampling to estimate bias and adjust the estimator accordingly. Jackknife methods estimate and remove bias by systematically leaving out parts of the data. Higher-order asymptotic corrections use additional terms in an expansion to reduce bias, especially for larger samples.

Applications occur across disciplines. In climate science, bias correction is used to adjust model outputs to better match observed distributions and to improve downscaling. In econometrics and statistics, bias correction addresses small-sample bias in estimators such as maximum likelihood estimates or nonlinear panel models. In predictive modeling more broadly, bias correction can improve forecast calibration and accuracy.

Bayesian and empirical Bayes approaches offer a different route to bias adjustment by incorporating prior information, yielding biased-but-potentially more accurate predictive distributions in some settings. These methods emphasize the trade-off between bias and variance.

A key consideration is the bias–variance trade-off: reducing bias can increase variance and affect overall mean squared error. Proper uncertainty quantification after bias correction is essential, and in some cases bias cannot be eliminated without unacceptable increases in variance.