Asymptotic behavior of least squares estimators for harmonics in multiplicative and additive noise

作者：Peng Huiming; Li Hongwei^*; Bian Jiawen

来源：Journal of Information and Computational Science, 2009, 6(4): 1847-1860.

• Asymptotic behaviors
• Asymptotic covariance matrix
• Asymptotic distributions
• Confidence interval
• Consistent estimators
• Finite samples
• Harmonics
• High-order
• Least-squares estimator
• Multicomponents
• Noise variance
• Numerical experiments
• Strong consistency
• Strong convergence
• Unknown parameters

In this paper the multi-component harmonics in multiplicative and additive noise is considered. Motivated by [5] and [28], we discuss the least squares estimators (LSEs) for the parameters of the considered model and obtain the strong consistency and high-order strong convergence rate of the LSEs. In addition, the asymptotic distribution of the LSEs is also derived, which can be used to obtain the confidence interval of the unknown parameters. Furthermore, we discuss the estimation of noise variance and obtain its strong consistency and asymptotic distribution. Finally some numerical experiments are performed to see how the asymptotic results behave for finite sample sizes.

• 出版日期2009