We consider the problem of estimating an
unknown density and its derivatives in a regression setting with random design.
Instead of expanding the function on a regular wavelet basis, we expand it on
the basis , a warped wavelet basis. We investigate the properties of this new
basis and evaluate its asymptotic performance by determining an upper bound of
the mean integrated squared error under different dependence structures. We
prove that it attains a sharp rate of convergence for a wide class of unknown regression
functions.
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, a warped wavelet basis. We investigate the properties of this new
basis and evaluate its asymptotic performance by determining an upper bound of
the mean integrated squared error under different dependence structures. We
prove that it attains a sharp rate of convergence for a wide class of unknown regression
functions.
