LAUSR

Using compactly supported wavelets, Gine and Nickl [Uniform limit theorems for wavelet density estimators, Ann. Probab. 37(4) (2009) 1605–1646] obtain the optimal strong L∞(ℝ) convergence rates of wavelet estimators for a fixed noise-free density function. They also study the same problem by spline wavelets [Adaptive estimation of a distribution function and its density in sup-norm loss by wavelet and spline projections, Bernoulli 16(4) (2010) 1137–1163]. This paper considers the strong Lp(ℝ)(1 ≤ p ≤∞) convergence of wavelet deconvolution density estimators. We first show the strong Lp consistency of our wavelet estimator, when the Fourier transform of the noise density has no zeros. Then strong Lp convergence rates are provided, when the noises are severely and moderately ill-posed. In particular, for moderately ill-posed noises and p = ∞, our convergence rate is close to Gine and Nickl’s.