Theoretical statistics and asymptotics
Theoretical statistics and asymptotics
This chapter sets out some ideas for incorporating into the teaching of theoretical statistics the advances made in the modern theory of parametric likelihood inference developed since the publication of Cox and Hinkley’s Theoretical Statistics. After a brief introduction, an account is given of likelihood-based asymptotics, marginal and conditional distributions, and the treatment of models with nuisance parameters using a local exponential family approximation to the statistical model of interest. Connections to Bayesian formulations, including the use of matching priors and computational aspects are discussed. The chapter concludes with a general discussion of higher order asymptotics and the role of other topics in the teaching of advanced statistical theory.
Keywords: asymptotic statistics, Bayesian statistics, higher order inference, parametric inference, likelihood, local exponential family, normal approximation, p* formula, pivot
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