Sufficiency

Charles A. Rohde
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Charles A. Rohde: Johns Hopkins University, Bloomberg School of Health

Chapter Chapter 11 in Introductory Statistical Inference with the Likelihood Function, 2014, pp 133-146 from Springer

Abstract: Abstract We consider a set of observations x thought to be a realization of some random variable X whose probability distribution belongs to a set of distributions ℱ = { f ( ⋅ ; θ ) : θ ∈ Θ } $$\displaystyle{\mbox{ $\boldsymbol{\mathcal{F}}$} =\{ f(\cdot \:;\:\theta )\::\:\theta \in \Theta \}}$$ The distributions in ℱ $$\mbox{ $\boldsymbol{\mathcal{F}}$}$$ are indexed by a parameter θ, i.e., the parameter θ determines which of the distributions is used to assign probabilities to X. The set Θ $$\Theta $$ is called the parameter space and ℱ $$\mbox{ $\boldsymbol{\mathcal{F}}$}$$ is called the family of distributions. ℱ $$\mbox{ $\boldsymbol{\mathcal{F}}$}$$ along with X constitutes the probability model for the observed data.

Keywords: Probability Model; Minimal Sufficient Statistic; Bernoulli Trials; Likelihood Inference; Likelihood Function (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-10461-4_11

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DOI: 10.1007/978-3-319-10461-4_11

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