Rates of convergence for the empirical quantization error
成果类型：
Article
署名作者：
Graf, S; Luschgy, H
署名单位：
University of Passau; Universitat Trier
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
发表日期：
2002
页码：
874-897
关键词：
摘要：
For n, k is an element of N and r > 0 let e(n,r)(P-k)(r) = inf (1)/(k)(kSigmai=1) parallel toX(i) - f(X-i)parallel to(r), where the infimum is taken over all measurable maps f:R-d --> R-d with \f(R-d)\ less than or equal to n and X-1,..., X-k are i.i.d. R-d-valued random variables. We analyse the asymptotic a.s. behaviour of the nth empirical quantization error e(n,r)(P-k).