ENTROPY AND PREFIXES
成果类型：
Article
署名作者：
SHIELDS, PC
署名单位：
Eotvos Lorand University
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/aop/1176989934
发表日期：
1992
页码：
403-409
关键词：
摘要：
Grassberger suggested an interesting entropy estimator, namely, n log n/SIGMA(i = 1)nL(i)n, where L(i)n is the shortest prefix of x(i), x(i + 1),..., which is not a prefix of any other x(j), x(j + 1), for j less-than-or-equal-to n. We show that this estimator is not consistent for the general ergodic process, although it is consistent for Markov chains. A weaker trimmed mean type result is proved for the general case, namely, given epsilon > 0, eventually almost surely all but an epsilon-fraction of the L(i)n/log n will be within epsilon of 1/H. A related Hausdorff dimension conjecture is shown to be false.