Optimal Estimation under Nonstandard Conditions

Optimal Estimation under Nonstandard Conditions

We 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 c...

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Bibliographic Details
Main Authors: PLOBERGER, Werner, PHILLIPS, Peter C. B.
Format: text
Language:English
Published: Institutional Knowledge at Singapore Management University 2012
Subjects:
Bayesian asymptotics
Asymptotic normality
Local asymptotic normality
Locally asymptotic quadratic
Optimality property of MLE
Weak convergence
Econometrics
Online Access:https://ink.library.smu.edu.sg/soe_research/1824
https://ink.library.smu.edu.sg/context/soe_research/article/2823/viewcontent/OptimalEstimationNonstandardConditions_2012.pdf
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Institution: Singapore Management University
Language: English
Description
Summary:We 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 Hajek-Le Cam optimality theory is adapted to cover this situation. We 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. Moreover, we demonstrate a direct connection between the (Bayesian property of) asymptotic normality of the posterior and the classical optimality properties of ML estimators. (C) 2012 Elsevier B.V. All rights reserved.

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