  Linear wavelet density estimators are wavelet projections of the empirical
measure based on independent, identically distributed observations. We study
here the law of the iterated logarithm (LIL) and a Berry-Esseen type theorem.
These results are proved under different assumptions on the density $f$ that
are different from those needed for similar results in the case of convolution
kernels (KDE): whereas the smoothness requirements are much less stringent than
for the KDE, Riemann integrability assumptions are needed in order to compute
the asymptotic variance, which gives the scaling constant in LIL. To study the
Berry-Esseen type theorem, a rate of convergence result in the martingale CLT
is used.
