Abstract
The problem of estimation of the derivative of a probability density f is considered, using wavelet orthogonal bases. We consider an important kind of dependent random variables, the so-called mixing random variables and investigate the precise asymptotic expression for the mean integrated error of the wavelet estimators. We show that the mean integrated error of the proposed estimator attains the same rate as when the observations are independent, under certain week dependence conditions imposed to the {X i}, defined in {Ω, N, P}.
Original language | English |
---|---|
Pages (from-to) | 195-203 |
Number of pages | 9 |
Journal | Statistical Papers |
Volume | 53 |
Issue number | 1 |
DOIs | |
Publication status | Published - Feb 2012 |
Externally published | Yes |
Keywords
- Mixing sequences
- Nonparametric estimation of a density
- Scaling function
- Wavelet function