A continuous mapping theorem for the argmax‐functional in the non‐unique case

Dietmar Ferger

Statistica Neerlandica, 2004, vol. 58, issue 1, 83-96

Abstract: The Argmax‐Continuous Mapping Theorem (Argmax‐CMT) of Kim and Pollard resp. van derVaart and Wellner has been proved to be a very useful tool in statistics for deriving distributional convergence of M‐estimators. However it only works as long as the limit process possesses an almost sure unique maximizing point. In this article we prove an extension of the Argmax‐CMT where almost sure uniqueness is no longer needed. Moreover our Argmax‐CMT is also valid in the function space D(ℝ) equipped with Lindvall’s version of the Skorokhod‐topology. As an example the result is applied to change‐point estimators.

Date: 2004
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