Mathematics – Statistics Theory
Scientific paper
2007-01-03
Statistical Science 2006, Vol. 21, No. 3, 363-375
Mathematics
Statistics Theory
Published at http://dx.doi.org/10.1214/088342305000000278 in the Statistical Science (http://www.imstat.org/sts/) by the Insti
Scientific paper
10.1214/088342305000000278
What role should assumptions play in inference? We present a small theoretical case study of a simple, clean case, namely the nonparametric comparison of two continuous distributions using (essentially) information about quartiles, that is, the central information displayed in a pair of boxplots. In particular, we contrast a suggestion of John Tukey--that the validity of inferences should not depend on assumptions, but assumptions have a role in efficiency--with a competing suggestion that is an aspect of Hansen's generalized method of moments--that methods should achieve maximum asymptotic efficiency with fewer assumptions. In our case study, the practical performance of these two suggestions is strikingly different. An aspect of this comparison concerns the unification or separation of the tasks of estimation assuming a model and testing the fit of that model. We also look at a method (MERT) that aims not at best performance, but rather at achieving reasonable performance across a set of plausible models.
Gastwirth Joseph L.
Krieger Abba M.
Rosenbaum Paul R.
Small Dylan S.
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