  Through the classical umbral calculus, we provide a unifying syntax for
single and multivariate $k$-statistics, polykays and multivariate polykays.
  From a combinatorial point of view, we revisit the theory as exposed by
Stuart and Ord, taking into account the Doubilet approach to symmetric
functions. Moreover, by using exponential polynomials rather than set
partitions, we provide a new formula for $k$-statistics that results in a very
fast algorithm to generate such estimators.
