Asymptotics and the theory of inference
The Annals of Statistics · 2003 · Volume 31 · Issue 6
Abstract
Asymptotic analysis has always been very useful for deriving distributions in statistics in cases where the exact distribution is unavailable. More importantly, asymptotic analysis can also provide insight into the inference process itself, suggesting what information is available and how this information may be extracted. The development of likelihood inference over the past twenty-some years provides an illustration of the interplay between techniques of approximation and statistical theory.
Keywords
$p$*, $P$-values, $r$*, 62-02, 62E20, 62F05, ancillarity, approximation, Bayesian inference, Conditioning, Laplace approximation, likelihood, matching priors, saddlepoint approximation, tail area, tangent exponential model
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