<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(2^{k_2}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mn>2</mn> <msub> <mi>k</mi> <mn>2</mn> </msub> </msup> </math></EquationSource> </InlineEquation> sub-models to at most <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(k_2\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>k</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation> 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.</p>

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Focused weighted-average least squares estimator

  • Shou-Yung Yin

摘要

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 \(2^{k_2}\) 2 k 2 sub-models to at most \(k_2\) 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.