Zhurakovskyi B.M.

Asymptotic Uniqueness of the Non-Linear Regression Model Parameter with Least Squares Estimator

In the paper the nonlinear regression model with continuous time and random noise, which is a local functional of strongly dependent stationary Gaussian random process, is considered. Sufficient conditions of asymptotic uniqueness of the least squares estimator of regression function parameters are obtained. This result is applied to the least squares estimator of amplitude and angular frequencies of harmonic oscillations sum observed on the background of given random noise.

Periodogram Estimator Properties of the Parameters of the Modulate almost Periodic Signal

The problem of detection of hidden periodicities is considered in the paper. In the capacity of useful signal model the modulated almost periodic signal is taken observed on the background of random noise being the local functional of Gaussian strongly dependent stationary process. For estimation of unknown amplitude and angular frequency of modulated signal periodogram estimators are chosen. Sufficient conditions on consistency and asymptotic normality of the estimators are obtained. The exact form of limiting normal distribution is found.

Periodogram Estimator Properties of the Parameters of the Regression Model with Strongly Dependent Noise

The problem of detection of hidden periodicities is considered in the paper. In the capacity of useful signal model the harmonic oscillation observed on the background of random noise, that is a local functional of Gaussian strongly dependent stationary process is taken. For estimation of unknown angular frequency and amplitude of harmonic oscillation periodogram estimator is chosen, for which sufficient conditions of asymptotic normality are obtained and limit normal distribution is found.

The estimator consistency of least squares parameters of a sum of harmonic oscillations in the models with strongly dependent noise

In this paper, we obtain sufficient conditions the estimator weak consistency of least squares amplitudes and angular frequencies of a sum of harmonic oscillations observed on the random noise background. We expect that the noise is a local functional of the Gaussian stationary strongly dependent process.