The Long March Toward Joint Asymptotics: My First Steps .

• Activity Number: 512
• Type: Invited
• Date/Time: Wednesday, August 7, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Noether Award Committee
• Author(s): Guang Cheng*+
• Companies: Purdue University

Abstract

We consider the joint asymptotics and inferences for the semi-nonparametric models where an Euclidean parameter and an infinite dimensional parameter are both of interest. The joint inferences, e.g., the prediction interval, are very useful in practice but its theoretical validity are very challenging to establish due to the different natures of two model components: parametric v.s. nonparametric. In this talk, we presents the fir?st comprehensive studies on the joint local/global inferences in a unified asymptotic framework. The inference optimality/e?efficiency issues are also carefully addressed. For simplicity of illustration, we use the generalized partly linear models (under penalized estimation) as the prototypical example. The novel joint Bahadur representation is developed as the theoretical foundation of all our results. This talk can be viewed as the first step to exploring the intriguing joint asymptotics phenomena in statistics.