By Dr. William J. J. Rey (auth.)
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Additional resources for Introduction to Robust and Quasi-Robust Statistical Methods
To ease the understanding of its analytical aspects, we now consider the three points just mentioned. The Prokhorov metric permits comparison of a discrete empirical distribution with a continuous one through the association of each observation of the former with a subset of the sample space; the comparison is then performed with the help of the probability of the latter distribution over this subset. ccordingly, the triangular inequality holds true. - Although we have required the possibility of considering simultaneously both types of distributions, we must say that several papers avoid this constraint and hence also avoid the Prokhorov metric.
2 I [n (n-1 ) ] + ... Obviously, the same mathematical trick can be applied to the second leading term of the expansion, and so on. To avoid a loss of efficiency in the estimation, he suggests the following definition of an average estimator =n a- [ (n-l ) In ] L: a,; For reasons that were not obvious at that time, the jackknife estimate 1) frequently exhibits fairly good statistical properties. Tukey who will soon appear on the stage has also named a,;, the pseudo-estimates, and 1),;, the jackknife pseUdo-values.
1. Introduction The so-called jackknife method has been introduced by Quenouille to reduce a bias in estimation and then progressively extended to obtain an estimate of variances. It is interesting in that it yields an improved estimator and enables the estimator to be assessed in an inexpensive way, that is with regard to the methodology although the computation, if required, is not necessarily inexpensive. By all standards the results thus obtained are impressive in most cases; but in a few, not very well defined, circumstances the results are either poor or ridiculous.