Asymptotic distribution of quadratic forms

• 成果类型: Article
• 署名作者: Götze, F; Tikhomirov, AN
• 署名单位: University of Bielefeld; Russian Academy of Sciences; Syktyvkar State University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 1999
• 页码: 1072-1098
• 关键词: limit-theorems; functionals; expansions

摘要

We consider quadratic forms [GRAPHICS] where X-j are i.i.d. random variables with finite third moment. We obtain optimal bounds for the Kolmogorov distance between the distribution of Q(n), and the distribution of the same quadratic forms with X-j replaced by corresponding Gaussian random variables. These bounds are applied to Toeplitz and random matrices as well. as to nonstationary AR(1) processes.