🤖 AI Summary
This study addresses the high computational complexity in focused model averaging arising from the exponential number of candidate submodels by proposing a computationally efficient, near-optimal Focused Weighted Least Squares (FWALS) estimator. The method introduces semi-orthogonalized auxiliary regressors to reduce the weight optimization problem to a regression scale proportional only to the number of auxiliary variables. It is solved using local zero-neighborhood asymptotic analysis, a plug-in AMSE criterion, and the Focused Information Criterion (FIC). Both theoretical analysis and simulation studies demonstrate that FWALS achieves stable performance—closely approximating the FIC benchmark—for focused targets such as impulse response functions, while substantially improving computational efficiency.
📝 Abstract
We propose a focused weighted-average least squares (FWALS) estimator that addresses the computational burden of focused model averaging. By semi-orthogonalizing auxiliary regressors, the weighting problem is reduced from $2^{k_2}$ sub-models to at most $k_2$ regressor-wise weights, yielding a tractable sub-optimal procedure. Under local-to-zero conditions, we derive the limiting distribution of FWALS for smooth focused functions and provide a plug-in AMSE criterion for data-driven weight selection. Simulations show that FWALS closely matches the focused information criterion (FIC) benchmark and delivers stable performance when focused function is designed for impulse response function. Prior-based WALS can be competitive in some settings, but its performance depends on the signal regime and the design of focused parameter. Overall, FWALS offers a practical and robust alternative with substantial computational savings.