Asymptotic Theory of the Least Squares Estimators of Sinusoidal Signal
作者:
Debasis Kundu,
期刊:
Statistics
(Taylor Available online 1997)
卷期:
Volume 30,
issue 3
页码: 221-238
ISSN:0233-1888
年代: 1997
DOI:10.1080/02331889708802611
出版商: Gordon & Breach Science Publishers
关键词: 62J02;62C05;Asymptotic distribution;strong consistency;least squares estimators and stationary distribution
数据来源: Taylor
摘要:
The consistency and the asymptotic normality of the least squares estimators are derived of the sinusoidal model under the assumption of stationary random error. It is observed that the model does not satisfy the standard sufficient conditions of Jennrich (1969), Wu (1981) or Kundu (1991). Recently the consistency and the asymptotic normality are derived for the sinusoidal signal under the assumption of normal error (Kundu; 1993) and under the assumptions of independent and identically distributed random variables in Kundu and Mitra (1996). This paper will generalize them. Hannan (1971) also considered the similar kind of model and establish the result after making the Fourier transform of the data for one parameter model. We establish the result without making the Fourier transform of the data. We give an explicit expression of the asymptotic distribution of the multiparameter case, which is not available in the literature. Our approach is different from Hannan's approach. We do some simulations study to see the small sample properties of the two types of estimators.
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