Reducing bias in nonparametric density estimation via bandwidth   dependent kernels: $L_1$ view
  We define a new bandwidth-dependent kernel density estimator that improves existing convergence rates for the bias, and preserves that of the variation, when the error is measured in $L_1$. No additional assumptions are imposed to the extant literature. 
Kairat Mynbaev and Carlos Martins-Filho
math.ST stat.TH