Jackknifing Kernel Type Density Estimators.
Technical rept. 1 Apr 1980-28 Feb 1983,
OHIO STATE UNIV COLUMBUS DEPT OF STATISTICS
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Jackknifing techniques are increasingly being applied to data analysis for bias reduction. In robust estimation, several studies have recently been published giving asymptotic properties of jackknifed estimates. Cheng has demonstrated the validity of jackknifing L-estimates under various conditions on the score function. Efron has shown that jackknife turns out to be special case of his bootstrap technique. In problems of density estimation, improvement of kernel type estimates was proposed by Schucany and Sommer through the technique of combining several estimates using different kernels. Usually it is possible to reduce bias in kernel-type estimates simply by a judicious choice of a kernel. However, in that case, the estimates of density functions can be negative. The situation has been described by Stute in his paper showing that the use of nonnegative kernels does not allow the possibility of reduction of bias. In this paper, the effect of jackknifing using leave-out rules, is studied. Pseudovalues in case of density estimates are defined and optimal properties of the jackknifed estimates are given. It is shown that the asymptotic behavior of the jackknifed estimates is the same as that of the classical estimate. A Berry-Esseen type central limit theorem showing the normality of the jackknifed estimate is also given. Author
- Statistics and Probability