RENORMALIZATION EXPONENTS AND OPTIMAL POINTWISE RATES OF CONVERGENCE

被引：66

作者：

DONOHO, DL ^{[1
]}

LOW, MG ^{[1
]}

机构：

[1] UNIV PENN,WHARTON SCH,DEPT STAT,PHILADELPHIA,PA 19104

来源：

ANNALS OF STATISTICS | 1992年 / 20卷 / 02期

关键词：

RADON TRANSFORM; RIESZ TRANSFORM; DECONVOLUTION; PARTIAL DECONVOLUTION; MINIMAX KERNELS; BOUNDARY KERNELS; MINIMAX LINEAR ESTIMATION; MINIMAX RISK; WHITE NOISE MODEL; GAUSSIAN EXPERIMENTS;

D O I：

10.1214/aos/1176348665

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Simple renormalization arguments can often be used to calculate optimal rates of convergence for estimating linear functionals from indirect measurements contaminated with white noise. This allows one to quickly identify optimal rates for certain problems of density estimation, nonparametric regression, signal recovery and tomography. Optimal kernels may also be derived from renormalization; we give examples for deconvolution and tomography.

引用

页码：944 / 970

页数：27

共 42 条

[1]

Adams RA., 2003, PURE APPL MATH SOB O, V2

[2] APPROXIMATION IN METRIC-SPACES AND ESTIMATION THEORY [J].