On the estimation of density-weighted average derivative by wavelet methods under various dependence structures - Archive ouverte HAL
Article Dans Une Revue Sankhya A Année : 2014

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, $\sqrt{\ln n /n}$ under the mean absolute error. A short simulation study illustrates the theory.
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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)

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Christophe Chesneau, Maher Kachour, Fabien Navarro. On the estimation of density-weighted average derivative by wavelet methods under various dependence structures. Sankhya A, 2014, ⟨10.1007/s13171-013-0032-1⟩. ⟨hal-00668544v3⟩
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