Open Access
February 2008 Mixed-rates asymptotics
Peter Radchenko
Ann. Statist. 36(1): 287-309 (February 2008). DOI: 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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Peter Radchenko. "Mixed-rates asymptotics." Ann. Statist. 36 (1) 287 - 309, February 2008.


Published: February 2008
First available in Project Euclid: 1 February 2008

zbMATH: 1131.62017
MathSciNet: MR2387972
Digital Object Identifier: 10.1214/009053607000000668

Primary: 60F17 , 62F12

Keywords: Empirical processes , K-means , Lasso , Limiting distribution , M-estimators , Nonstandard asymptotics , Partial splines , rates of convergence , shorth , singular quadratic approximation

Rights: Copyright © 2008 Institute of Mathematical Statistics

Vol.36 • No. 1 • February 2008
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