LIMIT THEOREMS FOR WEIGHTED NONLINEAR TRANSFORMATIONS OF GAUSSIAN STATIONARY PROCESSES WITH SINGULAR SPECTRA

• 成果类型: Article
• 署名作者: Ivanov, Alexander V.; Leonenko, Nikolai; Ruiz-Medina, Maria D.; Savich, Irina N.
• 署名单位: Ministry of Education & Science of Ukraine; Igor Sikorsky Kyiv Polytechnic Institute; Cardiff University; University of Granada
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/12-AOP775
• 发表日期: 2013
• 页码: 1088-1114
• 关键词: multiple stochastic integrals; REGRESSION-MODEL; steins method; functionals; FIELDS; CONVERGENCE; SEQUENCES; errors

摘要

The limit Gaussian distribution of multivariate weighted functionals of nonlinear transformations of Gaussian stationary processes, having multiple singular spectra, is derived, under very general conditions on the weight function. This paper is motivated by its potential applications in nonlinear regression, and asymptotic inference on nonlinear functionals of Gaussian stationary processes with singular spectra.