Large deviations of a correlogram estimator of the random noise covariance function in a nonlinear regression model
DOI:
https://doi.org/10.15407/dopovidi2016.09.023Keywords:
correlogram estimator, covariance function, nonlinear regression model, probability of large deviations, pseudometric, stationary Gaussian noiseAbstract
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.
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