Accession Number : ADA328320

Title :   Asymptotic Theory of the Least Squares Estimators of Sinusoidal Signal.

Descriptive Note : Technical rept.,

Corporate Author : PENNSYLVANIA STATE UNIV UNIVERSITY PARK CENTER FOR MULTIVARIATE ANALYSIS

Personal Author(s) : Kundu, Debasis

PDF Url : ADA328320

Report Date : JUL 1997

Pagination or Media Count : 16

Abstract : 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.

Descriptors :   *LEAST SQUARES METHOD, *ASYMPTOTIC NORMALITY, MATHEMATICAL MODELS, RANDOM VARIABLES, TIME SERIES ANALYSIS, REGRESSION ANALYSIS, ERROR ANALYSIS, ASYMPTOTIC SERIES, COVARIANCE, NORMAL DISTRIBUTION.

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE