A Note on Differentials and the CLT and LIL for Statistical Functions, with Application to $M$-Estimates
A Note on Differentials and the CLT and LIL for Statistical Functions, with Application to $M$-Estimates
A parameter expressed as a functional $T(F)$ of a distribution function (df) $F$ may be estimated by the "statistical function" $T(F_n)$ based on the sample df $F_n$. For analysis of the estimation error $T(F_n) - T(F)$, we adapt the differential approach of von Mises (1947) to exploit stochastic properties of …