Multidimensional Density Estimation by Tomography
本文将计算机断层扫描中的滤波反投影算法应用于多维密度的统计平滑，利用自动一维密度平滑器获得自动平滑的多维密度，无需可加性等结构假设，并在并行计算机上实现线性加速。
SUMMARY The paper explores the application of the filtered backprojection algorithm of computerized tomography to statistical smoothing of multidimensional densities. The method makes use of automated one-dimensional density smoothers to obtain an automated smoothed multidimensional density. No structural assumptions such as additivity or log-additivity are used. An important computational aspect of this method is its inherently parallel structure. We demonstrate linear speed-up on a parallel computer architecture. Various practical details are discussed together with some illustrative two-dimensional examples. Asymptotic mean error characteristics of the method are shown to match those of more familiar multivariate kernel-, near-neighbour- and spline-type smoothing techniques.