This paper considers estimation of the density function in the context of biased data using thresholded wavelet estimator. We adapt the method of estimating the square root of the density function as advocated in Pinheiro and Vidakovic (Comput Stat Data Anal 25:399–415, 1997) in the iid case. The density estimator is obtained by squaring the resulting estimator that as a result guarantees non-negativity. It is shown that the resulting estimator achieves the optimal $${\mathbb {L}}_2$$ L2 convergence in Besov spaces $$B_{pq}^s(M)$$ Bpqs(M) for $$p\ge 2$$ p≥2 whereas for $$p\in [1,2)$$ p∈[1,2) there is a logarithmic penalty attached to the optimal order. Finally, a simulation study shows that the resulting estimator may be favored over the usual wavelet estimator, with a proper choice of the preliminary estimator of the biased density.