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Mallows 模型平均的最优性AI 解读

In the past decades, model averaging (MA) has attracted much attention as it has emerged as an alternative tool to the model selection (MS) statistical approach. Hansen introduced a Mallows model averaging (MMA) method with model weights selected by minimizing a Mallows’ Cp criterion. The main theoretical justification for MMA is an asymptotic optimality (AOP), which states that the risk/loss of the resulting MA estimator is asymptotically equivalent to that of the best but…

模型平均能否改进模型选择？AI 解读

In regression, model averaging (MA) provides an alternative to model selection (MS), and asymptotic efficiency theories have been derived for both MS and MA. Basically, under sensible conditions, MS asymptotically achieves the smallest estimation loss/risk among the candidate models, and MA does so among averaged estimators from the models with convex weights. Clearly, MA can beat MS by any extent in rate of convergence when all the candidate models have large biases that…