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Plug-in estimators for higher-order transition densities in autoregression

Anton SchickWolfgang Wefelmeyer — 2009

ESAIM: Probability and Statistics

In this paper we obtain root- consistency and functional central limit theorems in weighted -spaces for plug-in estimators of the two-step transition density in the classical stationary linear autoregressive model of order one, assuming essentially only that the innovation density has bounded variation. We also show that plugging in a properly weighted residual-based kernel estimator for the unknown innovation density improves on plugging in an unweighted residual-based kernel...

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