A note on exact convergence rates in some martingale central limit theorems
成果类型：
Article
署名作者：
Renz, J
署名单位：
Michigan State University
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/aop/1065725195
发表日期：
1996
页码：
1616-1637
关键词：
摘要：
Bolthausen established a bound of order 1/root n on the rate of convergence in the central limit theorem for martingale difference arrays having bounded conditional moments of order 4. In the present paper it is shown how much this moment condition can be relaxed while maintaining the same rate of convergence. An example shows that, unlike in the i.i.d. case, a moment condition of order 3 is not enough. Furthermore, exact rates of convergence are derived for moment conditions of order between 2 and 3.