Distribution estimation under error-prone or non-ideal sampling modelled as "sticky" channels have been studied recently motivated by applications such as DNA computing. Missing mass, the sum of probabilities of missing letters, is an important quantity that plays a crucial role in distribution estimation, particularly in the large alphabet regime. In this work, we consider the problem of estimation of missing mass, which has been well-studied under independent and identically distributed (i.i.d) sampling, in the case when sampling is "sticky". Precisely, we consider the scenario where each sample from an unknown distribution gets repeated a geometrically-distributed number of times. We characterise the minimax rate of Mean Squared Error (MSE) of estimating missing mass from such sticky sampling channels. An upper bound on the minimax rate is obtained by bounding the risk of a modified Good-Turing estimator. We derive a matching lower bound on the minimax rate by extending the Le Cam method.

翻译：以“ 粘性” 频道为样样样,根据“ 粘性” 频道的差错或非理想抽样估计分布,最近根据DNA计算等应用方法进行了研究。 缺失质量,即缺失字母概率之和,是一个重要的数量,在分布估计中起着关键作用,特别是在大字母制中。 在这项工作中,我们考虑了缺失质量估算问题,在独立和同样分布( i.d) 抽样下,这种估算得到了很好研究,在取样为“ 粘性” 的情况下,这种估算是“ 粘性” 。 准确地说,我们考虑了一个未知分布的每个样本反复出现几何分布次数的情况。 我们从这种粘性取样渠道中描述估计缺失质量的平方错误( MSE) 的微缩缩缩速率。 微缩缩缩鼠比率的上限是通过将修改的“ 粘液” 方法与微缩压速率相匹配。