Theory of Probability and Mathematical Statistics
(Teoriya Imovirnostei ta Matematychna Statystyka)
Stochastic asymptotic expansion of correlogram estimator of the correlation function of random noise in nonlinear regression model
O. V. Ivanov, K. K. Moskvichova
Abstract: A correlogram estimator of the covariance function of a stationary Gaussian noise is considered in a nonlinear regression model with continuous time. The estimator is constructed from deviations of the observed stochastic process from the regression function where the least squares estimator is substituted for the unknown parameter. A stochastic asymptotic expansion of the correlogram estimator of the covariance function is obtained for the case where the time of observations tends to infinity.
Keywords: Nonlinear regression model with continuous time, stationary Gaussian noise, covariance function, least squares estimator, stochastic asymptotic expansion
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