Large Deviations Of The Correlogram Estimator Of The Random Noise Covariance Function In The Nonlinear Regression Model

In the paper an exponential bound for the probabilities of large deviations of the normalized residual correlogram as an estimator of a random stationary Gaussian noise covariance function in continuous time nonlinear functional regression model is obtained. The strongest known result on weak consistency of the residual correlogram is a corollary of this fact.