Open Access
2011 A continuous mapping theorem for the smallest argmax functional
Emilio Seijo, Bodhisattva Sen
Electron. J. Statist. 5: 421-439 (2011). DOI: 10.1214/11-EJS613


This paper introduces a version of the argmax continuous mapping theorem that applies to M-estimation problems in which the objective functions converge to a limiting process with multiple maximizers. The concept of the smallest maximizer of a function in the d-dimensional Skorohod space is introduced and its main properties are studied. The resulting continuous mapping theorem is applied to three problems arising in change-point regression analysis. Some of the results proved in connection to the d-dimensional Skorohod space are also of independent interest.


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Emilio Seijo. Bodhisattva Sen. "A continuous mapping theorem for the smallest argmax functional." Electron. J. Statist. 5 421 - 439, 2011.


Published: 2011
First available in Project Euclid: 10 May 2011

zbMATH: 1329.60090
MathSciNet: MR2802050
Digital Object Identifier: 10.1214/11-EJS613

Keywords: Change-point , compound Poisson process , Cox proportional hazards model , multiple maximizers , Skorohod spaces with multidimensional parameter

Rights: Copyright © 2011 The Institute of Mathematical Statistics and the Bernoulli Society

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