Theory of Probability and Mathematical Statistics
Stochastic asymptotic expansion of correlogram estimator of the correlation function of random noise in nonlinear regression model
O. V. Ivanov, K. K. Moskvichova
Download PDF
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
Bibliography: 1. A. V. Ivanov, Asymptotic Theory of Nonlinear Regression, Kluwer Academic Publishers, Dordrecht-Boston-London, 1997.
2. O. V. Ivanov and I. K. Matsak, Limit theorems for the maximal residuals in linear and nonlinear regression models, Teor. Imovirnost. Matem. Statyst. 86 (2012), 81-91; English transl. in Theor. Probability and Math. Statist. 86 (2013), 79-91.
3. A. V. Ivanov and N. N. Leonenko, Statistical Analysis of Random Fields, Vyshcha shkola'', Kiev, 1986; English transl., Kluwer Academic Publishers, Dordrecht, 1989.
4. V. V. Buldygin and Yu. V. Kozachenko, Metric Characterization of Random Variables and Random Processes, TViMS'', Kiev, 1998; English transl., American Mathematical Society, Providence, RI, 2000.
5. I. I. Gihman and A. V. Skorohod, Introduction to the Theory of Random Processes, ''Nauka'', Moscow, 1965; English transl., Saunders, Philadelphia, 1969.
