A continuous mapping theorem for the smallest argmax functional. (English) Zbl 1329.60090

Summary: 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 Skorokhod 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 Skorokhod space are also of independent interest.


60G07 General theory of stochastic processes
62G35 Nonparametric robustness
Full Text: DOI arXiv Euclid


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