Groupe d’études et de recherche en analyse des décisions

On the minimax optimality of block thresholded wavelet estimators with long memory data

Linyuan Li

We consider the estimation of nonparametric mean regression function with long memory data and investigate the asymptotic rates of convergence of estimators based on block thresholding. We show that the estimators achieve optimal minimax convergence rates over a large classes of functions that involve many irregularities of a wide variety of types, including chip and Doppler functions, and jump discontinuities. Therefore, wavelet estimators provide extensive adaptivity to many irregularities of large function classes. This work is an extension of Hall et al (1998, 1999) from i.i.d. error to long range dependence error.

Reference: Hall, P., Kerkyacharian, G. and Picard, D. (1998). Block threshold rules for curve estimation using kernel and wavelet method. Ann. Statist. 26, 922-942. Hall, P., Kerkyacharian, G. and Picard, D. (1999). On the minimax optimality of block thresholded wavelet estimators. Statistica Sinica, 9, 33-50.