AISM 53, 159-178
© 2001 ISM
(Received April 14, 2000; revised August 16, 2000)
Abstract. Wavelet methods are used to estimate density and (auto-) regression functions that are possibly discontinuous. For stationary time series that satisfy appropriate mixing conditions, we derive mean integrated squared errors (MISEs) of wavelet-based estimators. In contrast to the case for kernel methods, the MISEs of wavelet-based estimators are not affected by the presence of discontinuities in the curves. Applications of this approach to problems of identification of nonlinear time series models are discussed.
Key words and phrases: Convergence rate, density estimation, nonparametric regression, piecewise-smoothness, wavelet.
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