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Statistica Sinica 15(2005), 177-195





WEIGHTED RESIDUAL-BASED DENSITY ESTIMATORS

FOR NONLINEAR AUTOREGRESSIVE MODELS


Ursula U. Müller, Anton Schick and Wolfgang Wefelmeyer


Universität Bremen, Binghamton University and Universität zu Köln


Abstract: This paper considers residual-based and randomly weighted kernel estimators for innovation densities of nonlinear autoregressive models. The weights are chosen to make use of the information that the innovations have mean zero. Rates of convergence are obtained in weighted $L_1$-norms. These estimators give rise to smoothed and weighted empirical distribution functions and moments. It is shown that the latter are efficient if an efficient estimator for the autoregression parameter is used to construct the residuals.



Key words and phrases: Efficient estimator, empirical likelihood estimator, Owen estimator, plug-in estimator, weighted residual-based density estimator.



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