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Abstract:
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One benefit of model averaging is that it incorporates rather than ignores the uncertainty in the model selection process. One of the most important and challenging aspects of model averaging is how to optimally combine estimates from different models. In this work, we propose a procedure to obtain optimal weight choice for frequentist model average estimators with respect to the mean squared error (MSE). As a basis for demonstrating our idea, we consider averaging over a sequence of linear regression models. Many model averaging methods are based on ordinary least squares (OLS) estimators. However, it is well known that the James-Stein (JS) estimator dominates the OLS estimator under quadratic loss, provided that the dimension of the parameter is greater than two. Motivated by the James-Stein estimator, we adaptively shrink the OLS estimator towards either the narrow model or the full model, and select the weights that minimize the model average estimator's estimated MSE. Asymptotic optimality of the proposed method is investigated. A Monte Carlo study based on simulated data evaluates and compares the finite sample properties of this mechanism with those of the existing methods.
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