Before revision:  We propose a new method - Weighted Inference by Model Plausibility (WIMP) - that takes rank uncertainty into account in a fully data-driven way and outperforms all other methods considered in the simulation study. The WIMP method is shown to deliver intervals that are robust to rank uncertainty, yet allow for meaningful inference, approaching fixed rank intervals when evidence for a particular rank is strong.
After revision:  We propose a new method - Weighted Inference by Model Plausibility (WIMP) - that takes rank uncertainty into account in a fully data-driven way and outperforms all other methods considered , delivering intervals that are robust to rank uncertainty, yet allow for meaningful inference, approaching fixed rank intervals when evidence for a particular rank is strong.