This is a somewhat unorthodox book, but a welcome one. It is about the application - yes, the application - of the higher order asymptotics of likelihood theory. Everyone is familiar with the use of basic large-sample likelihood asymptotics (asymptotic normality, Fisher information, and all that) to provide approximate hypothesis tests and confidence intervals. Higher order asymptotics, which has seen much theoretical development over the last 20 years or so, extends the familiar 'first-order asymptotics' with a view to improving the quality of asymptotic inference. This endeavour is quite successful, but not entirely trivial to apply or understand.
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