Analysis of Mallows model averaging with non-unique optimal mixtures

Analyze coverage guarantees and weight convergence for Algorithm 1 when Mallows model averaging is applied and the population prediction loss \(\mathcal{C}_\infty(\mathbf w)\) has multiple minimizers on the simplex, leading to non-unique optimal mixes and potentially random limiting weights.

Background

The paper proves $\sqrt{n}$-rate convergence of Mallows weights under standard time-series conditions when either a single model uniquely minimizes the population KLIC or a unique mixture minimizes the population prediction loss.

However, when several mixtures yield the same population risk, the limiting weights need not be unique and may remain random. The authors explicitly leave the theoretical analysis of the algorithm in this non-unique minimizer case for future work.