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We investigate the estimation of a weighted density taking the form g = w(F)f , where f denotes an unknown density, F the associated distribution function and w is a known non-negative weight. Such a class encompasses many examples, including those arising in order statistics or when g is related to the maximum or the minimum of N (random or fixed)… (More)

We observe n heteroscedastic stochastic processes {Yv(t)}v, where for any v ∈ {1,. .. , n} and t ∈ [0, 1], Yv(t) is the convolution product of an unknown function f and a known blurring function gv corrupted by Gaussian noise. Under an ordinary smoothness assumption on g 1 ,. .. , gn, our goal is to estimate the d-th derivatives (in weak sense) of f from… (More)

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… (More)

The nonparametric estimation of the m-fold convolution power of an unknown function f is considered. We introduce an estimator based on a plug-in approach and a wavelet hard thresholding estimator. We explore its theoretical asymptotic performances via the mean integrated squared error assuming that f has a certain degree of smoothness. Applications and… (More)

- Fabien Navarro
- 2013

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