Abstract
Higher-order likelihood methods often give very accurate results. A way to evaluate accuracy is the comparison of the solutions with the exact ones of the classical theory, when these exist. To this end, we consider inference for a scalar regression parameter in the normal regression setting. In particular, we compare confidence intervals computed from the likelihood and its higher-order modifications with the ones based on the Studentt distribution. It is shown that higher-order likelihood methods give accurate approximations to exact results.
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Sartori, N. A note on likelihood asymptotics in normal linear regression. Ann Inst Stat Math 55, 187–195 (2003). https://doi.org/10.1007/BF02530493
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DOI: https://doi.org/10.1007/BF02530493