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Optimal Estimation Under Nonstandard Conditions

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Executive Summary

The authors analyze optimality properties of Maximum Likelihood (ML) and other estimators when the problem does not necessarily fall within the Locally Asymptotically Normal (LAN) class, therefore covering cases that are excluded from conventional LAN theory such as unit root nonstationary time series. The classical H?jek-Le Cam optimality theory is adapted to cover this situation. They show that the expectation of certain monotone "Bowl-shaped" functions of the squared estimation error are minimized by the ML estimator in locally asymptotically quadratic situations, which often occur in nonstationary time series analysis when the LAN property fails.

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