The Reduction of Bias in Parametric Estimation.
SOUTHERN METHODIST UNIV DALLAS TEX DEPT OF STATISTICS
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A general class of transformations of estimators is introduced which induces a reduction in bias if any exists. The concept is related to that of the sequence to sequence transformations which are employed for convergence improvement in deterministic cases such as the evaluation of infinite series and improper integrals. The procedure introduced by Quenouille 1949, 1956 and later termed the jackknife by Tukey 1958 is seen to be a special case of these transformations. The general principles of the method produce insight into the applications where the ordinary jackknife is not trustworthy. To illustrate the method and to demonstrate its potential usefulness, several examples are considered. For ratio estimation under a particular model a new unbiased estimator is produced which exhibits a favorable mean square error relative to existing adjusted estimators. The existing notion of reapplication of such a procedure is shown to lack the property for which it was designed. Proper reapplication is proposed so as to conform to general principles. A higher order transformation is defined which provides an interesting algorithm for the corrected procedure. Possible extensions to nonlinear transformations are also mentioned. Author
- Statistics and Probability