In this note we introduce a new estimator for estimating autoregressive model function based on two-dimensional wavelet expansion of joint density function. We investigate some asymptotic properties of the proposed estimator. We also added the problem of estimating of derivative of autoregressive estimator through new approach. Finally, we apply our method in dynamical systems. In particular, we estimate a chaotic map from a noisy data and filter entropy of the chaotic map.
|Number of pages||24|
|Journal||Italian Journal of Pure and Applied Mathematics|
|Publication status||Published - Dec 2010|
- Besov space
- multiresolution analysis
- random design
- two-dimensional wavelet