Electronic Journal of Statistics

A continuous mapping theorem for the smallest argmax functional

Emilio Seijo and Bodhisattva Sen

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Abstract

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.

Article information

Source
Electron. J. Statist. Volume 5 (2011), 421-439.

Dates
First available in Project Euclid: 10 May 2011

Permanent link to this document
http://projecteuclid.org/euclid.ejs/1305034909

Digital Object Identifier
doi:10.1214/11-EJS613

Mathematical Reviews number (MathSciNet)
MR2802050

Zentralblatt MATH identifier
06166829

Citation

Seijo, Emilio; Sen, Bodhisattva. A continuous mapping theorem for the smallest argmax functional. Electron. J. Statist. 5 (2011), 421--439. doi:10.1214/11-EJS613. http://projecteuclid.org/euclid.ejs/1305034909.


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