"Some results on linearization and normal approximation of combinatorial
statistics"
Given a finite set of size N, consider a real function defined on subsets of
size n. Draw a random subset (uniformly distributed over the class of
subsets of size n) and evaluate the function. Let T denote the value
obtained. T is (called) a symmetric statistic based on sample (of size n)
drawn without replacement from a finite population (of size N). In order to
analyse/approximate the distribution of T the statistic is decomposed into
the sum of mutually uncorrelated parts:
T = Linear+Quadratic + Cubic+ ... called Hoeffding's decomposition. For
example, using the approximation
T = Linear one shows the asymptotic normality of T (as n,N->infty).
Similarly the approximation T = Linear+Quadratic leads to the normal
approximation + Edgeworth correction term.