Weighted-average least squares (WALS) is a powerful and computationally efficient model-averaging method that simultaneously accounts for the noise generated by model selection and estimation. Its baseline setup is a classical linear regression model with two subsets of regressors: the focus regressors, which are included on theoretical or other substantive grounds, and the auxiliary regressors, whose inclusion is less certain.
WALS departs from other model-averaging techniques in two key respects. First, it applies a semi-orthogonal transformation to the auxiliary regressors, which substantially reduces the computational burden typical of classical model-averaging estimators. Second, it employs a non-standard Bayesian shrinkage approach to the normal location model, which ensures desirable theoretical properties such as admissibility, bounded risk, robustness, optimality in terms of minimax regret, and uniform sqrt-n consistency.
WALS delivers a comprehensive inferential toolkit, encompassing point estimation, prediction, estimation of sampling moments (bias, standard error, and root mean squared error), and the construction of confidence and prediction intervals. Moreover, the baseline model with iid errors has been extended in various directions to accommodate heteroscedasticity, serial correlation, panel data structures, and generalized linear models.