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Abstract:
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In this talk we investigate how `non-standard' estimators (i.e., estimators that converge in distribution to a non-normal limit at a rate slower than square-root n) behave under a sample-splitting strategy, the so-called `divide-and-conquer' method --- partition the available data into subsamples, compute an estimate from each subsample and combine these appropriately to form the final estimator --- that has been much used in the analysis of large data sets. We show that in some non-standard problems sample-splitting can not only ameliorate the computational difficulties, but can also lead to improved inference and more precise estimation.
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