Canadian Journal of Statistics

Information, ancillarity, and sufficiency in the presence of nuisance parameters

Journal Article

Abstract

The Fisher information about parameters of interest (P‐information) is invariant with respect to nuisance parameters, and induces an information inequality associated with likelihood factorization. This information inequality provides a natural basis for measuring information loss due to using only a sublikelihood function for inference. In contrast with the global reparametrization of some previous concepts in the literature, the concepts of P‐ancillarity and P‐sufficiency proposed in this article are characterized by the notion of no pointwise information loss with respect to the parameters of interest. A conditional version of P‐sufficiency is also proposed. The asymptotic efficiency of likelihood inference under P‐ancillarity or P‐sufficiency is outlined.

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