Maximum Likelihood Estimation for Dependent Observations

The asymptotic properties of m.l.e. are discussed for generally dependent observations. Conditions are derived for weak consistency and asymptotic Normality of the estimates. We further consider the case where some of the parameters are "transient" in the sense that the accumulated informa...

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Bibliographic Details
Published in:Journal of the Royal Statistical Society. Series B, Methodological Methodological, 1976, Vol.38 (1), p.45-53
Main Author: Crowder, Martin J.
Format: Article
Language:English
Subjects:
asymptotic normality
Asymptotic properties
Central limit theorem
consistency
Consistent estimators
Covariance matrices
dependent observations
Infinity
Martingales
Mathematical independent variables
Maximum likelihood estimation
Maximum likelihood estimators
transient parameters
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Summary:The asymptotic properties of m.l.e. are discussed for generally dependent observations. Conditions are derived for weak consistency and asymptotic Normality of the estimates. We further consider the case where some of the parameters are "transient" in the sense that the accumulated information on them from the sample does not increase indefinitely; then the interest lies in estimating the other parameters consistently. Examples are given, and the work is related to that of Neyman and Scott (1948).
ISSN:0035-9246
1369-7412
2517-6161
1467-9868
DOI:10.1111/j.2517-6161.1976.tb01565.x