  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.
