  Standardness is a popular assumption in the literature on set estimation. It
also appears in statistical approaches to topological data analysis, where it
is common to assume that the data were sampled from a probability measure that
satisfies the standard assumption. Relevant results in this field, such as
rates of convergence and confidence sets, depend on the standardness parameter,
which in practice may be unknown. In this paper, we review the notion of
standardness and its connection to other geometrical restrictions. We prove the
almost sure consistency of a plug-in type estimator for the so-called
standardness constant, already studied in the literature. We propose a method
to correct the bias of the plug-in estimator and corroborate our theoretical
findings through a small simulation study. We also show that it is not possible
to determine, based on a finite sample, whether a probability measure satisfies
the standard assumption.
