ASYMPTOTIC DISTRIBUTION OF MAXIMUM LIKELIHOOD ESTIMATORS IN LINEAR MODELS WITH AUTOREGRESSIVE DISTURBANCES.
RAND CORP SANTA MONICA CALIF
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Hildreth and Lu proposed a method for obtaining maximum likelihood estimates of linear model coefficients whose disturbances are generated by a stationary linear first-order autoregressive process with unknown autoregression coefficient. Until the present study was performed, consistency was the only property that had been shown for these estimates. This memorandum shows that the estimates of coefficients of independent variables and the estimate of the autoregression coefficient have a limiting joint multivariate-normal distribution, with the estimate of autoregression distributed independently of the estimates of coefficients of independent variables. This asymptotic covariance matrix of these latter estimates is the same as that of the best linear unbiased estimates for a model in which the autoregression coefficient is known. Author
- Statistics and Probability