Limit theorems for weighted nonlinear transformations of Gaussian stationary processes with singular spectra

• Autores: Alexander V. Ivanov, Nikolai Leonenko , María D. Ruiz-Medina, Irina N. Savich
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 41, Nº. 2, 2013, págs. 1088-1114
• Idioma: inglés
• DOI: 10.1214/12-AOP775
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• Resumen

  • 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.