# Likelihood and auxiliary statistics

Chapter

## Abstract

Let (*X*, p(x;ω), Ω) be a parametric statistical model, which we shall denote by *M*. Here *X* is the sample space, Ω is the parameter space, and p(x;ω) is the model function. We presume the existence of a measure *μ* on *X* such that for each fixed value of the parameter ω the function p(x;ω) is the density with respect to *μ* of a probability measure P_{ω} on *X*, and we term x → p(x;ω) the probability function corresponding to ω. The parameter space Ω is a subset of d-dimensional Euclidean space R^{d} and we denote coordinates of ω by ω^{r},ω^{s},…, the indices r,s,… thus running from 1 to d. Throughout, Ω will be either an open set or such a set with some of its boundary points added.

## Keywords

Likelihood Function Maximum Likelihood Estimator Auxiliary Statistic Profile Likelihood Inverse Gaussian Distribution
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Copyright information

© Springer-Verlag Berlin Heidelberg 1988