On the relationship between higher-order stochastic expansions, influence functions and U-statistics for M-estimators.

It is shown that higher-order influence functions for M-estimators are mathematically equivalent to higher-order stochastic approximations to these estimators. The stochastic expansions are also shown to have corresponding higher-order U-statistic representations, providing an alternative approach for deriving and analyzing the approximate properties of M-estimators. [ABSTRACT FROM AUTHOR]