Higher order kernels in adaptive location estimation*

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In the semiparametric location model, an adaptive location estimate can be obtained by plugging kernel estimates of density and its derivative into the one-step approximation of the parametric maximum likelihood estimate. In this paper, we investigate the effect of higher order kernels on second order asymptotics of the adaptive location estimate. The optimal order of bandwidths in terms of estimating the location parameter are established. We also give some simulation results to see the effect of higher order kernels for moderate sample sizes.