WAVELET-BASED ESTIMATORS OF THE INTEGRATED SQUARED DENSITY DERIVATIVES FOR MIXING SEQUENCES
Nargess Hosseinioun, Hassan Doosti, Hossein Ali Niroumand · 2009
The problem of estimation of the squared derivative of a probability density f is considered using wavelet orthogonal bases. We obtain the precise asymptotic expression for the mean integrated error of the wavelet estimators when the process is strongly mixing. We show that the proposed estimator attains the same rate as when the observations are independent. Certain week dependence conditions are imposed to the {}iX defined in { , ,}N P .