The Annals of Mathematical Statistics

Asymptotic Distribution of Maximum Likelihood Estimators in a Linear Model With Autoregressive Disturbances

Clifford Hildreth

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Abstract

It is shown that maximum likelihood estimators of parameters of a linear model with autoregressive disturbances have an asymptotic multivariate normal distribution with mean vector equal to the true parameter values. Inspection of the variance matrix shows that the estimators are asymptotically efficient and that the estimates of coefficients of the independent variables have the same variance matrix as the best unbiased estimates for a modified model in which the autocorrelation parameter is known. It is conjectured that the asymptotic distribution of the estimates of coefficients of independent variables may be a useful approximation for moderate sized samples. Alternative approximations for the estimates of the autoregression coefficient and the variance are suggested for further study.*

Article information

Source
Ann. Math. Statist., Volume 40, Number 2 (1969), 583-594.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177697726

Digital Object Identifier
doi:10.1214/aoms/1177697726

Mathematical Reviews number (MathSciNet)
MR243663

Zentralblatt MATH identifier
0174.22801

JSTOR
links.jstor.org

Citation

Hildreth, Clifford. Asymptotic Distribution of Maximum Likelihood Estimators in a Linear Model With Autoregressive Disturbances. Ann. Math. Statist. 40 (1969), no. 2, 583--594. doi:10.1214/aoms/1177697726. https://projecteuclid.org/euclid.aoms/1177697726


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