Can you rephrase the following email in a polite, clear, and convincing manner:

Thank you for your feedback and for considering our submission JRSSB-Jan-2025-0054. We appreciate the opportunity to submit our work to JRSS-B.

We are writing to express some concerns regarding the review process for our manuscript. While we fully acknowledge that our submission is not without areas for improvement, we were disappointed by the overall quality and depth of the reviews received, particularly given the high standards typically associated with JRSS-B.

In our case, we received two reviews: one generally positive and one more critical with two concerns. The Associate Editor (AE)’s decision appears to have relied primarily on the two claims from the critical review and added a third point that, unfortunately, seems to contradict even the reviewer's own assessment. We believe all three key criticisms are based on misreadings of the manuscript, which we detail below.

We recognise that editorial decisions are challenging and based on many factors, but we are particularly concerned because the core critiques—on which the rejection seems to rest—are factually incorrect and addressed clearly in the manuscript. For completeness, we have attached a brief document highlighting these points with references to specific sections of the paper.

    Novelty of the Algorithmic Framework

The algorithmic framework is not novel, as the only improvement is on the score function. The proof techniques are the same. – Reviewer and AE

This statement overlooks the central contribution of the paper: a generalised framework that interpolates between previously published methods, offering a flexible spectrum of trade-offs between validity and statistical variability. This extension leads to new theoretical results (e.g., Table 5), based on different proof techniques than those used in our ICML 2023 work. These points are outlined in the abstract, introduction, and Sections 4–5.

    Value of Impossibility Results

Impossibility results are useless because the intuition existed. – AE

While some intuition existed for the first impossibility result, a formal proof—particularly one showing a square-root rate—was lacking in the literature. Moreover, the subsequent results in Section 2.2 (acknowledged as solid and interesting by the reviewer) go well beyond prior intuitions and show limitations that were previously unproven. The AE’s critique also misrepresents our handling of MCAR vs. MAR: our results precisely show that going beyond MCAR is provably infeasible under certain conditions. These points are outlined in the introduction and Section 2.

    Omission of Contributions in Sections 3 and 5

The methodological part of this paper is exclusively MCAR. – Reviewer and AE These sections, including comprehensive experiments under MCAR, MAR, MNAR, and other realistic settings, were not acknowledged in the AE report. The reviewer stated that “the methodological part of this paper is exclusively MCAR,” which is demonstrably incorrect (this is outlined before Section 5, e.g. in the introduction and Table 2). We raise these points not to challenge editorial discretion, but because we believe the decision was based on demonstrable inaccuracies. This is particularly disheartening given the care we put into this work—and especially for me as corresponding author, having recently invested substantial time in reviewing another JRSS-B submission (JRSSB-Oct-2024-0581), where I ensured thoughtful and thorough feedback despite early reservations about fit.

We hope this note and the attached document are helpful in clarifying our concerns. We would be grateful if the editorial team could reconsider the decision, or at least acknowledge the issues raised in the process.

Thank you again for your time and for your ongoing work in maintaining the high standards of JRSS-B.

Best regards,