Conditioning out rare events for exponential families has negligible effect on inference. Issue 16 (17th August 2016)

• Record Type: Journal Article
• Authors: Withers, Christopher S.; Nadarajah, Saralees
• Is Part Of: Communications in statistics. Volume 45:Issue 16(2016)
• Page Start: 4886
• Page End: 4895
• Publication Date: 2016-08-17
• Subjects: Binomial distribution -- Cumulants -- Multinomial distribution -- Negative multinomial distribution.; 62E99; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2014.932807
• Languages: English
• ISSNs: 0361-0926

Abstract

ABSTRACT: Suppose that we observe X ∼Binomial( n, p ). Inference on p is difficult if X = 0 or n . One way around this is to condition on these events not happening. We show that this has only an exponentially small effect on its cumulants. This is also true if we condition away other rare events. Our results are presented for exponential families, with applications to the binomial, multinomial and negative multinomial distributions.