The price of bias reduction when there is no unbiased estimate. (English) Zbl 0669.62010

Doss, Hani; Sethuraman, Jayaram

Ann. Stat. 17, No. 1, 440-442 (1989).

Let \(\Phi\) be a parameter for which there is no unbiased estimator. This note shows that for an arbitrary sequence of estimators \(T^{(k)}\), if te biases of \(T^{(k)}\) tend to 0 then their variances must tend to \(\infty\).

MSC:

62F10	Point estimation
62A01	Foundations and philosophical topics in statistics

Keywords:

bias reduction; jackknife estimate of bias; bootstrap estimate of bias