A CONSISTENT APPROACH TO LEAST SQUARES ESTIMATION OF CORRELATION DIMENSION IN WEAK BERNOULLI DYNAMICAL SYSTEMS
成果类型：
Article
署名作者：
Serinko, Regis J.
署名单位：
Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/aoap/1177004914
发表日期：
1994
页码：
1234-1254
关键词：
摘要：
A new approach to the least squares procedure for correlation dimension estimation is suggested. Consistency of the new estimator is established for a class of dynamical systems that includes the Cantor map and the logistic map with parameter value 4. Unlike the proofs of consistency for other estimation procedures, no assumptions are made about the Grassberger-Procaccia spatial correlation integral beyond the existence of the correlation dimension.