  arXiv:2206.10812v1 [stat.ME] proposes a useful algorithm, named generalized
Diversity Subsampling (g-DS) algorithm, to select a subsample following some
target probability distribution from a finite data set and demonstrates its
effectiveness numerically. While the asymptotic performances of g-DS when the
true data distribution is known was discussed in arXiv:2206.10812v1 [stat.ME],
it remains an interesting question how the estimation errors in the density
estimation step, which is an unavoidable step to use g-DS in real-world data
sets, influences its asymptotic performance. In this paper, we study the
pointwise convergence rate of probability density function (p.d.f) the g-DS
subsample to the target p.d.f value, as the data set size approaches infinity,
under consideration of the pointwise bias and variance of the estimated data
p.d.f.
