On the integrated squared error of the linear wavelet density estimator

•We study here the integrated squared error of the linear wavelet density estimator.•We provide a law of the iterated logarithm of the concentration about its mean.•We obtain a polynomial upper bound for the rate of convergence in the CLT.

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∥L2(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).