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Asymptotics for Wavelet Based Estimates of Piecewise Smooth Regression for Stationary Time Series |
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| Authors: | Young K. Truong Prakash N. Patil |
| Affiliation: | (1) Department of Biostatistics, The University of North Carolina at Chapel Hill, Chapel Hill, NC, 27599-7400, USA, e-mail;(2) Department of Statistics and Applied Probability, National University of Singapore, 3 Science Drive 2, Singapore, 117543, Singapore;(3) School of Mathematics and Statistics, The University of Birmingham, Birmingham, B15 2TT, UK |
| 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. |
| Keywords: | Convergence rate density estimation nonparametric regression piecewise-smoothness wavelet |
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