Abstract
We extend the results of De Luca et al. (2021) to inference for linear regression models based on weighted-average least squares (WALS), a frequentist model averaging approach with a Bayesian flavor. We concentrate on inference about a single focus parameter, interpreted as the causal effect of a policy or intervention, in the presence of a potentially large number of auxiliary parameters representing the nuisance component of the model. In our Monte Carlo simulations we compare the performance of WALS with that of several competing estimators, including the unrestricted least-squares estimator (with all auxiliary regressors) and the restricted least-squares estimator (with no auxiliary regressors), two post-selection estimators based on alternative model selection criteria (the Akaike and Bayesian information criteria), various versions of frequentist model averaging estimators (Mallows and jackknife), and one version of a popular shrinkage estimator (the adaptive LASSO). We discuss confidence intervals for the focus parameter and prediction intervals for the outcome of interest, and conclude that the WALS approach leads to superior confidence and prediction intervals, but only if we apply a bias correction.
Highlights
Data are generated by a potentially complex process, the so-called data-generating process (DGP), usually represented by a joint probability distribution over the sample space
In this paper we have attempted to extend the theory of weighted-average least squares (WALS) estimation to inference
A key ingredient in this extension is the use of bias correction in WALS, as introduced in De Luca et al (2021)
Summary
Data are generated by a potentially complex process, the so-called data-generating process (DGP), usually represented by a joint probability distribution over the sample space. The current paper extends their results to inference by proposing a simulation-based approach for WALS confidence and prediction intervals. This approach yields re-centered intervals, using the bias-corrected posterior mean as a frequentist estimator of the normal location parameter. The main conclusion of our Monte Carlo experiment is that, compared to other estimators, coverage errors for WALS are small and confidence and prediction intervals are short, centered correctly, and allow for asymmetry. They are easy and fast to compute by simulation. Appendix A contains the abbreviations used in the paper, and Appendix B describes the main algorithm for simulation-based WALS confidence intervals
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