A continuous mapping theorem for the smallest argmax functional

作者：Seijo Emilio^*; Sen Bodhisattva

来源：Electronic Journal of Statistics, 2011, 5: 421-439.

DOI：10.1214/11-EJS613

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

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.

• 出版日期2011