Functional convergence and optimality of plug-in estimators for stationary densities of moving average processes

Schick, Anton; Wefelmeyer, Wolfgang

Bernoulli, Tome 10 (2004) no. 2, p. 889-917 / Harvested from Project Euclid

Résumé

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 n^1/2-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.

Publié le : 2004-10-14
Classification: efficient estimator, functional central limit theorem, least dispersed estimator, plug-in estimator, semiparametric model, time series

@article{1099579161,
     author = {Schick, Anton and Wefelmeyer, Wolfgang},
     title = {Functional convergence and optimality of plug-in estimators for stationary densities of moving average processes},
     journal = {Bernoulli},
     volume = {10},
     number = {2},
     year = {2004},
     pages = { 889-917},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1099579161}
}

Schick, Anton; Wefelmeyer, Wolfgang. Functional convergence and optimality of plug-in estimators for stationary densities of moving average processes. Bernoulli, Tome 10 (2004) no. 2, pp.  889-917. http://gdmltest.u-ga.fr/item/1099579161/