Estimation in autoregressive model with measurement error

Abstract : Consider an autoregressive model with measurement error: we observe $Z_i=X_i+\varepsilon_i$, where $X_i$ is a stationary solution of the equation $X_i=f_{\theta^0}(X_{i-1})+\xi_i$. The regression function $f_{\theta^0}$ is known up to a finite dimensional parameter $\theta^0$. The distributions of $X_0$ and $\xi_1$ are unknown whereas the distribution of $\varepsilon_1$ is completely known. We want to estimate the parameter $\theta^0$ by using the observations $Z_0,\ldots,Z_n$. We propose an estimation procedure based on a modified least square criterion involving a weight function $w$, to be suitably chosen. We give upper bounds for the risk of the estimator, which depend on the smoothness of the errors density $f_\varepsilon$ and on the smoothness properties of $w f_\theta$.
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Article dans une revue
ESAIM: Probability and Statistics, EDP Sciences, 2014, ESAIM Probability and Statistics 18, pp.277-307
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Contributeur : Marie-Luce Taupin <>
Soumis le : lundi 24 octobre 2011 - 12:24:31
Dernière modification le : mardi 10 octobre 2017 - 11:22:03
Document(s) archivé(s) le : mercredi 25 janvier 2012 - 02:30:54

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  • HAL Id : hal-00591114, version 2
  • ARXIV : 1105.1310

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Jérôme Dedecker, Adeline Samson, Marie-Luce Taupin. Estimation in autoregressive model with measurement error. ESAIM: Probability and Statistics, EDP Sciences, 2014, ESAIM Probability and Statistics 18, pp.277-307. 〈hal-00591114v2〉

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