Asymptotic properties of the weighted average least squares (WALS) estimator

Arbeitspapier

We investigate the asymptotic behavior of the WALS estimator, a model-averaging estimator with attractive finite-sample and computational properties. WALS is closely related to the normal location model, and hence much of the paper concerns the asymptotic behavior of the estimator of the unknown mean in the normal local model. Since we adopt a frequentist-Bayesian approach, this specializes to the asymptotic behavior of the posterior mean as a frequentist estimator of the normal location parameter. We emphasize two challenging issues. First, our definition of ignorance in the Bayesian step involves a prior on the t-ratio rather than on the parameter itself. Second, instead of assuming a local misspecification framework, we consider a standard asymptotic setup with fixed parameters. We show that, under suitable conditions on the prior, the WALS estimator is sqrt(n)-consistent and its asymptotic distribution essentially coincides with that of the unrestricted least-squares estimator. Monte Carlo simulations confirm our theoretical results.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Tinbergen Institute Discussion Paper ; No. TI 2022-022/III

Classification and Topics

• Classification: Wirtschaft ; Bayesian Analysis: General ; Estimation: General ; Model Construction and Estimation ; Model Evaluation, Validation, and Selection
• Subject: Model averaging ; normal location model ; consistency ; asymptotic normality ; WALS

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): De Luca, Giuseppe ; Magnus, Jan ; Peracchi, Franco
• Event: Veröffentlichung
• (who): Tinbergen Institute
• (where): Amsterdam and Rotterdam
• (when): 2022

Further information

• Handle: http://hdl.handle.net/10419/263942
• Last update: 10.03.2025, 11:43 AM CET