Wavelet-Based Density Estimation in a Heteroscedastic Convolution Model

Abstract

We consider a heteroscedastic convolution density model under the “ordinary smooth assumption.” We introduce a new adaptive wavelet estimator based on term-by-term hard thresholding rule. Its asymptotic properties are explored via the minimax approach under the mean integrated squared error over Besov balls. We prove that our estimator attains near optimal rates of convergence (lower bounds are determined). Simulation results are reported to support our theoretical findings.

Keywords:

• Density deconvolution
• Hard thresholding
• Heteroscedasticity
• Lower bounds
• Rates of convergence
• Wavelet bases

Mathematics Subject Classification:

• 62G07
• 62G20

Acknowledgment

This work is supported by ANR grant NatImages, ANR-08-EMER-009.