Abstract
We give new results, under mild assumptions, on convergence rates in L1 and L2 for residual-based kernel estimators of the innovation density of moving average processes. Exploiting the convolution representation of the stationary density of moving average processes, these estimators can be used to obtain n1/2-consistent plug-in estimators for this stationary density. Here we derive functional weak convergence results in L1 and C0(R) for these plug-in estimators. If efficient estimators for the finite-dimensional parameters of the process are used in our construction, semiparametric efficiency of our plug-in estimators is obtained.
Citation
Anton Schick. Wolfgang Wefelmeyer. "Functional convergence and optimality of plug-in estimators for stationary densities of moving average processes." Bernoulli 10 (5) 889 - 917, October 2004. https://doi.org/10.3150/bj/1099579161
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