Deconvolution Density Estimation with Penalized MLE
提出一种在无限维函数空间上优化惩罚似然的新方法，用于从含测量误差的样本中估计分布，在小样本或低信噪比下优于现有方法，并首次给出惩罚最大似然估计的相合性和收敛速度。
Deconvolution is the important problem of estimating the distribution of a quantity of interest from a sample with additive measurement error. Nearly all infinite-dimensional deconvolution methods in the literature use Fourier transformations. These methods are mathematically neat, but unstable, and produce bad estimates when signal-noise ratio or sample size are low. A popular alternative is to maximize penalized likelihood for a finite-dimensional basis expansion of the unknown density. We develop a new method to optimize penalized likelihood over the infinite-dimensional space of all functions. This gives the stability of regularized likelihood methods without restricting the space of solutions. Our method compares favorably with state-of-the-art methods on simulated and real data, particularly for small sample size or low signal-noise ratio. We also provide the first results on the consistency and rate of convergence of penalized maximum likelihood estimates for density deconvolution. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.