Risk-efficient nonparametric sequential estimators
Let \(x_ 1,x_ 2,x_ 3,..\). be a sequence of independent identically distributed random variables and \(\tau\) an estimable parameter of their distribution. We want to estimate \(\tau\) by the corresponding U-statistic \(u_ n\) with loss function \((u_ n-\tau)^ 2+cn\). We derive a stopping time and prove its risk-efficiency in the sense of \textit{N. Starr} [Ann. Math. Stat. 37, 1173-1185 (1966; Zbl 0144.408)] without any assumption on the nature of the distribution function other than the existence of some moments.
scientific article; zbMATH DE number 3986474
scientific article