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Asymptotic Normmality of Maximum Likelihood Estimators Obtained from Normally Distributed but Dependent Observations

Published online by Cambridge University Press:  18 October 2010

Risto D. H. Heijmans and
Jan R. Magnus
Risto D. H. Heijmans
Affiliation:
University of Amsterdam
Jan R. Magnus
Affiliation:
London School of Economics
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Abstract

In this article we aim to establish intuitively appealing and verifiable conditions for the first-order efficiency and asymptotic normality of ML estimators in a multi-parameter framework, assuming joint normality but neither the independence nor the identical distribution of the observations. We present five theorems (and a large number of lemmas and propositions), each being a special case of its predecessor.

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Articles
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Econometric Theory , Volume 2 , Issue 3 , December 1986, pp. 374 - 412
Copyright
Copyright © Cambridge University Press 1986

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References

REFERENCES

1.Anderson, T. W.The statistical analysis of time series. New York: John Wiley, 1971.Google Scholar
2.Apostol, T. M.Mathematical analysis (2nd edition). Reading, Mass.: Addison-Wesley, 1974.Google Scholar
3.Cramer, H.Mathematical methods of statistics. Princeton: Princeton University Press, 1946.Google Scholar
4.Hannan, E. J.Multiple time series. New York: John Wiley, 1970.CrossRefGoogle Scholar
5.Hannan, E. J.The asymptotic theory of linear time-series models. Journal of Applied Probability 10 (1973): 130–145.CrossRefGoogle Scholar
6.Heijmans, R.D.H. and Magnus., J. R.On the first-order efficiency and asymptotic normality of maximum likelihood estimators obtained from dependent observations. Statistica Neerlandica 40 (1986): 169–188.CrossRefGoogle Scholar
7.Heijmans, R.D.H. and Magnus., J. R.Consistent maximum-likelihood estimation with dependent observations: the general (non-normal) case and the normal case. Journal of Econometrics 32 (1986): 253–285.CrossRefGoogle Scholar
8.Hildreth, C.Asymptotic distribution of maximum likelihood estimators in a linear modelwith autoregressive disturbances. Annals of Mathematical Statistics 40 (1969): 583–594.CrossRefGoogle Scholar
9.Holly, A. Problem 85.1.2. Econometric Theory 1 (1985): 143–144. Solution in Econometric Theory 2 (1986): forthcoming.CrossRefGoogle Scholar
10.Magnus, J. R.Maximum likelihood estimation of the GLS model with unknown parameters in the disturbance covariance matrix. Journal of Econometrics 1 (1978): 281–312. Corrigenda in: Journal of Econometrics 10 (1979): 261.CrossRefGoogle Scholar
11.Magnus, J. R. and Neudecker., H.The commutation matrix: some properties and applications. The Annals of Statistics 7 (1979): 381–394.CrossRefGoogle Scholar
12.Malinvaud, E.Statistical methods of econometrics (2nd edition). Amsterdam: North-Holland, 1970.Google Scholar
13.Mann, H. B. and Wald., A.On the statistical treatment of linear stochastic difference equations. Econometrica 11 (1943): 173–220.CrossRefGoogle Scholar
14.Marcus, M. and Minc, H.. A survey of matrix theory and matrix inequalities. Boston: Allyn and Bacon, 1964.Google Scholar
15.Poincaré, H.Calcul des probabilités (2nd edition). Paris, 1912.Google Scholar
16.Rao, C. R.Linear statistical inference and its applications (2nd edition). New York: John Wiley, 1973.CrossRefGoogle Scholar
17.Rozanov, Yu. A.Stationary random processes. San Francisco: Holden-Day, 1967.Google Scholar
18.Rubin, H.Some results on the asymptotic distribution of maximum- and quasi-maximumlikelihood estimates (abstract). Annals of Mathematical Statistics 19 (1948): 598.Google Scholar
19.Schönfeld, P.A useful central limit theorem for m-dependent variables. Metrika 17 (1971): 116–128.CrossRefGoogle Scholar
20.Weiss, L.Asymptotic properties of maximum likelihood estimators in some nonstandard cases, II. Journal of the American Statistical Association 68 (1973): 428–430.CrossRefGoogle Scholar