Bernoulli

  • Bernoulli
  • Volume 10, Number 5 (2004), 889-917.

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

Anton Schick and Wolfgang Wefelmeyer

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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.

Article information

Source
Bernoulli, Volume 10, Number 5 (2004), 889-917.

Dates
First available in Project Euclid: 4 November 2004

Permanent link to this document
https://projecteuclid.org/euclid.bj/1099579161

Digital Object Identifier
doi:10.3150/bj/1099579161

Mathematical Reviews number (MathSciNet)
MR2093616

Zentralblatt MATH identifier
1058.62072

Keywords
efficient estimator functional central limit theorem least dispersed estimator plug-in estimator semiparametric model time series

Citation

Schick, Anton; Wefelmeyer, Wolfgang. Functional convergence and optimality of plug-in estimators for stationary densities of moving average processes. Bernoulli 10 (2004), no. 5, 889--917. doi:10.3150/bj/1099579161. https://projecteuclid.org/euclid.bj/1099579161


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