On the estimation of density-weighted average derivative by wavelet methods under various dependence structures - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2012

On the estimation of density-weighted average derivative by wavelet methods under various dependence structures

Résumé

The problem of estimating the density-weighted average derivative of a regression function is considered. We present a new consistent estimator based on a plug-in approach and wavelet projections. Its performances are explored under various dependence structures on the observations: the independent case, the $\rho$-mixing case and the $\alpha$-mixing case. More precisely, denoting $n$ the number of observations, in the independent case, we prove that it attains $1/n$ under the mean squared error, in the $\rho$-mixing case, $1/\sqrt{n}$ under the mean absolute error, and in the $\alpha$-mixing case, and $\sqrt{\ln n /n}$ under the mean absolute error.
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Dates et versions

hal-00668544 , version 1 (09-02-2012)
hal-00668544 , version 2 (23-02-2012)
hal-00668544 , version 3 (31-05-2013)

Identifiants

  • HAL Id : hal-00668544 , version 2

Citer

Christophe Chesneau, Maher Kachour. On the estimation of density-weighted average derivative by wavelet methods under various dependence structures. 2012. ⟨hal-00668544v2⟩
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