In recent years, a growing number of online retail companies have embraced deep learning models for demand forecasting, leveraging their scalability in processing large-scale datasets. Accurate demand forecasts enable improved planning and allow operational flexibility to adjust sales accordingly. Moreover, quantile estimation has gained widespread application as it offers valuable uncertainty quantification, thereby enhancing the robustness of decision-making processes. However, limited research has addressed the effective quantification of uncertainty when target labels are ambiguous. In retail, actual sales can be capped by stock and boosted by temporary promotions, whereas the target is underlying demand. Such scenarios are characterized by double censoring and no deep-learning pipeline yet exists for such data. In this paper, we introduce a straightforward framework for learning quantiles from doubly-censored observations and propose a tailored evaluation metric. Our approach is supported by theoretical guarantees, and we empirically demonstrate that our metric correlates well with the oracle calibration measure. Experimental results show that our estimator surpasses existing baselines. Finally, inventory simulations and real-world applications confirm the practical utility of our method in retail operations.

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