Computer intensive methods in adaptive contexts

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The advent of fast computing has allowed statisticians to develop new statistical methods which would have been unthinkable just a few years ago because it would have been impossible to use them in practice.  One example is the class of resampling methods which can be used to compute estimates of the variance of a complicated estimator, approximate confidence intervals or even choose tuning parameters in cases where an estimator is only defined up to a tuning parameter which must be determined.  The main objective of this research program is to improve the theoretical and practical understanding of these methods so as to develop sound new statistical procedures. One important project is as follows.  When studying a certain phenomenon, data are collected to learn about the distribution of the variable of interest.  Often, other data from a related study or from previous years exist.  Because of different conditions or changes over time, these additional data often come from a similar albeit different distribution.  If the distributions are quite similar, rather than ignoring these other data, it may be worthwhile to try to combine them with the data under study.  The method of maximum weighted likelihood (MWL) attempts exactly that.  By weighting differently the observations whether they come from the phenomenon under study or from one of the competing samples, the MWL estimator can trade some bias for much improved precision.  The difficulty is in choosing the appropriate weights.  Wang and Zidek (2005) have suggested using cross-validation, but noted that their method does not work when the competing samples all come from the same distribution.  This is not surprising considering the work of Altman and Léger (1997) on tuning parameter selection and the rate of convergence of estimators.  To alleviate the problem, the bootstrap will be used to choose the weights.  This method will work even when the distributions are identical.  This will provide an interesting solution to this practical problem, and will open new grounds for the method of MWL.