Large deviations of a correlogram estimator of the random noise covariance function in a nonlinear regression model

1Moskvychova, KK
1National Technical University of Ukraine "Kyiv Polytechnic Institute"
Dopov. Nac. akad. nauk Ukr. 2016, 9:23-28
https://doi.org/10.15407/dopovidi2016.09.023
Section: Mathematics
Language: Ukrainian
Abstract: 

A time continuous nonlinear regression model with mean square continuous and almost sure Gaussian stationary random noise with zero mean and positive bounded spectral density is considered. A theorem on probabilities of large deviations of a residual correlogram estimator of the random noise covariance function is proved. The result obtained sharpens previously known facts on the consistency of a correlogram estimator of the covariance function of Gaussian stationary random noise.

Keywords: correlogram estimator, covariance function, nonlinear regression model, probability of large deviations, pseudometric, stationary Gaussian noise
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