OPTIMAL RATES OF CONVERGENCE FOR NONPARAMETRIC STATISTICAL INVERSE PROBLEMS

• 成果类型: Article
• 署名作者: KOO, JY
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176349138
• 发表日期: 1993
• 页码: 590-599
• 关键词: regression; EQUATIONS; noisy

摘要

Consider an unknown regression function f of the response Y on a d-dimensional measurement variable X. It is assumed that f belongs to a class of functions having a smoothness measure p. Let T denote a known linear operator of order q which maps f to another function T(f) in a space G. Let T(n) denote an estimator of T(f) based on a random sample of size n from the distribution of (X, Y), and let \\T(n)-T(f)\\G be a norm of T(n)-T(f). Under appropriate regularity conditions, it is shown that the optimal rate of convergence for \\T(n)-T(f)\\G is n-(p-q)/(2p+d). The result is applied to differentiation, fractional differentiation and deconvolution.