Nonstandard M-Estimation Under Partially Identified Models

• Activity Number: 71
• Type: Contributed
• Date/Time: Sunday, August 9, 2015 : 4:00 PM to 5:50 PM
• Sponsor: IMS
• Author(s): Han Jiang* and Stephen Man Sing Lee
• Companies: and The University of Hong Kong
• Keywords: M-estimation ; Partial identification ; Bootstrap

Abstract

It is well known in an M-estimation setting that when the criterion function is non-regular, a non-Gaussian limiting distribution often results, rendering conventional resampling methods inconsistent. Inferences of this kind become even more formidable under partial identification settings in which the functional of interest can range over a proper set rather than be identified uniquely as a singleton. Certain classes of partially identified models, such as those characterized by moment inequalities, have been extensively studied in the literature, while inferences remain prohibitive outside such restrictive contexts. In the present paper, we investigate inference procedures based on non-regular M-estimators under different partially identified structures. By adapting a criterion-function-like approach originally proposed for partially identified models subject to moment inequality conditions, we develop confidence procedures for a general class of M-estimation problems unexplored so far. Our procedures are illustrated with applications to non-studentized location estimation and least quantile of squares estimation, in the presence of missing observations.