STRONG CONVERGENCE PROBLEM FOR CUMULANT ESTIMATORS IN HARMONIC RETRIEVAL
谐波恢复中累量估计的强收敛问题

This paper considers the single record estimators for cumulants of sinusoids in additive noise. The strong convergence of sample autocorrelation is proved, and the convergence rate is obtained. Conditions for the fourth-order ergodicity are given. Under these conditions, the strong convergence of sample estimates of the fourth-order moment and cumulant is established, and the convergence rate is obtained. Finally, a numerical example is given to verify the results.