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Consistency of Maximum Likelihood Estimators When Observations Are Dependent

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  • Heijmans, R
  • Magnus, J

Abstract

Wald's (1949) classical consistency theorem (which proves strong consistency of the maximum likelihood estimator when the observations are independent and identically distributed) is extended to cover the case of dependent observations. Three consistency theorems for dependent observations are proved under conditions which, in our opinion, are weaker (and more readily applicable) than usual: (i) the regularity conditions do not involve derivatives of the likelihood function, (ii) no uniform convergence assumption is made, (iii) the parameter space need not be compact, (iv) the number of parameters, though fixed and finite, is arbitrary, and (v) the true distribution underlying the observations need not be specified.

Suggested Citation

  • Heijmans, R & Magnus, J, 1983. "Consistency of Maximum Likelihood Estimators When Observations Are Dependent," University of Amsterdam, Actuarial Science and Econometrics Archive 293066, University of Amsterdam, Faculty of Economics and Business.
    • Handle: RePEc:ags:amstas:293066
    DOI: 10.22004/ag.econ.293066
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    Research Methods/ Statistical Methods;

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