Wavelet regression estimations with strong mixing data

摘要

Using a wavelet basis, we establish in this paper upper bounds of wavelet estimation on L p(Rd) risk of regression functions with strong mixing data for 1 = p infinity. In contrast to the independent case, these upper bounds have different analytic formulae for p. [1, 2] and p. (2,+infinity). For p = 2, it turns out that our result reduces to a theorem of Chaubey et al. (J Nonparametr Stat 25: 53-71, 2013); and for d = 1 and p = 2, it becomes the corresponding theorem of Chaubey and Shirazi (Commun Stat Theory Methods 44: 885-899, 2015).