Mixed-rates asymptotics

Details Mixed-rates asymptotics Mixed-rates asymptotics

2008-03-13

arxiv.org/abs/0803.1942v1

Annals of Statistics 2008, Vol. 36, No. 1, 287-309

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/009053607000000668 the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053607000000668

A general method is presented for deriving the limiting behavior of estimators that are defined as the values of parameters optimizing an empirical criterion function. The asymptotic behavior of such estimators is typically deduced from uniform limit theorems for rescaled and reparametrized criterion functions. The new method can handle cases where the standard approach does not yield the complete limiting behavior of the estimator. The asymptotic analysis depends on a decomposition of criterion functions into sums of components with different rescalings. The method is explained by examples from Lasso-type estimation, $k$-means clustering, Shorth estimation and partial linear models.

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