Abstract
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 ρ-mixing case and the α-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 ρ-mixing case, \(1/\sqrt{n}\) under the mean absolute error, and, in the α-mixing case, \(\sqrt{\ln n /n}\) under the mean absolute error. A short simulation study illustrates the theory.
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Chesneau, C., Kachour, M. & Navarro, F. On the estimation of density-weighted average derivative by wavelet methods under various dependence structures. Sankhya A 76, 48–76 (2014). https://doi.org/10.1007/s13171-013-0032-1
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DOI: https://doi.org/10.1007/s13171-013-0032-1
Keywords and phrases.
- Nonparametric estimation of density-weighted average derivative
- ‘plug-in’ approach, wavelets
- consistency
- ρ-mixing
- α-mixing