This paper is motivated by the need to quantify human immune responses to
environmental challenges. Specifically, the genome of the selected cell
population from a blood sample is amplified by the well-known PCR process of
successive heating and cooling, producing a large number of reads. They number
roughly 30,000 to 300,000. Each read corresponds to a particular rearrangement
of so-called V(D)J sequences. In the end, the observation consists of a set of
numbers of reads corresponding to different V(D)J sequences. The underlying
relative frequencies of distinct V(D)J sequences can be summarized by a
probability vector, with the cardinality being the number of distinct V(D)J
rearrangements present in the blood. Statistical question is to make inferences
on a summary parameter of the probability vector based on a single
multinomial-type observation of a large dimension. Popular summary of the
diversity of a cell population includes clonality and entropy, or more
generally, is a suitable function of the probability vector. A point estimator
of the clonality based on multiple replicates from the same blood sample has
been proposed previously. After obtaining a point estimator of a particular
function, the remaining challenge is to construct a confidence interval of the
parameter to appropriately reflect its uncertainty. In this paper, we have
proposed to couple the empirical Bayes method with a resampling-based
calibration procedure to construct a robust confidence interval for different
population diversity parameters. The method has been illustrated via extensive
numerical study and real data examples