A retailer cannot sell more than it has in stock; therefore, its sales observations are a censored representation of the underlying demand process. When a retailer forecasts demand based on past sales observations, it requires an estimation approach that accounts for this censoring. Several authors have analyzed inventory management with demand learning in environments with censored observations, but the authors assume that inventory levels are known and hence that stockouts are observed. However, firms often do not know how many units of inventory are available to meet demand, a phenomenon known as inventory record inaccuracy. We investigate the impact of this unknown on demand estimation in an environment with censored observations. When the firm does not account for inventory uncertainty when estimating demand, we discover and characterize a systematic downward bias in demand estimation under typical assumptions on the distribution of inventory record inaccuracies. We propose and test a heuristic prescription that relies on a single error statistic and that sharply reduces this bias.