Fernholz L.T. von Mises Calculus For Statistical Functionals

Springer, 1983. — 124 p.About forty years ago, Richard von Mises proposed a theory for the analysis of the asymptotic behavior of nonlinear statistical functionals based on the differentiability properties of these functionals. His theory was largely neglected until the late 1960's when it experienced a renaissance due to developments in the field of robust statistics. In particular, the "Volterra" derivative used by von Mises evolved into the influence curve, which was used to provide information about the sensi- ti vity of an estimator to outliers, as well as the estimator's asymptot- ic variance. Moreover, with the "Princeton Robustness Study" (Andrews et al. (1972)), there began a proliferation of new robust statistics, and the formal von Mises calculations provided a convenient heuristic tool for the analysis of the asymptotic distributions of these statistics.Von Mises’ Method.
Hadamard Differentiation.
Some Probability Theory on C[0,1] and D[0,1].
M-, L-, and R-Estimators.
Calculus on Function Spaces.
Applications.
Asymptotic Efficiency.