Abstract
This paper is concerned with the estimation of a parameter of a stochastic process on the basis of a single realization. It is shown, under suitable regularity conditions, that the maximum likelihood estimator is the best consistent asymptotically normal estimator in the sense of having minimum asymptotic variance. It also produces the best limiting probability of concentration in symmetric intervals. An application is given for the problem of estimating the mean of the offspring distribution in a Galton-Watson branching process.
Received 13 October 1977
Revised 24 April 1978
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Heyde, C.C. (2010). On an Optimal Asymptotic Property of the Maximum Likelihood Estimator of a Parameter from a Stochastic Process. In: Maller, R., Basawa, I., Hall, P., Seneta, E. (eds) Selected Works of C.C. Heyde. Selected Works in Probability and Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-5823-5_44
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DOI: https://doi.org/10.1007/978-1-4419-5823-5_44
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