A note on some exact jackknife and bootstrap estimators

The remarkable evolution in computer technology in the last three decades, the high speed and the power of the new generation of computers stimulated the development of the so-called computer intensive statistical methods. Bootstrap method has rapidly gain popularity among statisticians, becoming a very useful tool in many practical situations, especially when small samples are available and the traditional asymptotical approach fails in providing reliable results. In this paper we discuss some particular examples of jackknife and bootstrap estimators that can be derived analytically. Since these estimators admit an exact formula, their computation does not require numerical approximation by,Monte Carlo simulations.