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MAXIMUM SMOOTHED LIKELIHOOD ESTIMATION

E. L. Ionides
Statistica Sinica
Vol. 15, No. 4 (October 2005), pp. 1003-1014
Stable URL: http://www.jstor.org/stable/24307347
Page Count: 12
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MAXIMUM SMOOTHED LIKELIHOOD ESTIMATION
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Abstract

Looking myopically at the larger features of the likelihood function, absent some fine detail, can theoretically improve maximum likelihood estimation. Such estimators are, in fact, used routinely, since numerical techniques for maximizing a computationally expensive likelihood function or for maximizing a Monte Carlo approximation to a likelihood function may be unable to investigate small scale behavior of the likelihood. A class of maximum smoothed likelihood estimators is introduced and shown to be asymptotically efficient for models possessing local asymptotic normality. This theoretical result corresponds to good finite sample properties in two examples, with a likelihood that is smooth but multimodal, and a likelihood that is not smooth.

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