Conditioning out rare events for exponential families has negligible effect on inference

Christopher S. Withers and Saralees Nadarajah

Communications in Statistics - Theory and Methods, 2016, vol. 45, issue 16, 4886-4895

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.

Date: 2016
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DOI: 10.1080/03610926.2014.932807

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