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\noindent Statistica Sinica {\bf 15}(2005), 1003-1014

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\centerline{\large\bf MAXIMUM SMOOTHED LIKELIHOOD ESTIMATION}
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\author{E. L. Ionides}
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\centerline{\it University of Michigan}
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\begin{quotation}
\noindent {\it 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.\par
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\noindent {\it Key words and phrases:}
Likelihood, local
asymptotic normality, maximum likelihood
estimation, maximum smoothed likelihood estimation, smoothing.\par
\end{quotation}

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