Metaestimers

Metaestimers, or meta-estimators, are estimators whose objective is to estimate properties of other estimators rather than directly estimating a population parameter. Formally, a metaestimator targets quantities such as the bias, variance, mean squared error, or the sampling distribution of a set of candidate estimators. The concept emphasizes evaluating and comparing estimation procedures themselves, rather than the underlying parameter.

Construction of metaestimers typically relies on resampling, simulation, or analytical approximations. Bootstrap and subsampling can provide bias and variance estimates for a given estimator; cross-validation and related risk estimation procedures yield expected predictive performance. In some frameworks, the delta-method or sandwich estimators provide analytic approximations to the variance of estimators, forming metaestimates when the parameters of interest depend on estimated quantities. Ensemble methods such as stacking often rely on metaestimates of estimator risk to assign weights to base learners.

Applications of metaestimation include model selection, estimator comparison, and the construction of improved estimators through weighting or combination of candidates. It is used in meta-analyses of methods, algorithm benchmarking, and automated machine learning pipelines where the goal is to select or calibrate estimators based on estimated performance rather than direct parameter estimation.

Limitations and notes: The accuracy of metaestimates depends on the validity of underlying assumptions (such as independence and identical distribution of samples) and the quality of the resampling or approximation methods. In finite samples or with complex dependence structures, metaestimates can be biased or unstable. The term metaestimer is not universally standardized, and related ideas may be described in terms of resampling-based risk estimation, estimator evaluation, or model selection criteria.