On the integrated squared error of the linear wavelet density estimator

The object of this paper is to study some asymptotic properties of the integrated squared error of a linear wavelet density estimator, ∥ f ^ n − f ∥ L 2 ( R ) 2 . We provide the exact almost sure rate of concentration about its mean, in fact a law of the iterated logarithm. Regarding the rate in probability, we obtain a polynomial upper bound for the rate of convergence in the central limit theorem of Zhang and Zheng (1999).