Abstract
Abstract In this chapter we consider the problem of constructing higher-order asymptotic approximations to the distribution of the maximum likelihood estimate, the likelihood ratio test statistic, and related quantities. Two basic methods are considered: Edge worth expansions and saddle point approximations. Edge worth expansions are discussed in Sections 5.3–5.5 and saddle point approximations are discussed in Section 5.6; approximations for the conditional distribution of likelihood-based quantities given an ancillary statistic will be considered in Chapter 6.
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