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Some comments concerning a curious singularity

Published online by Cambridge University Press:  14 July 2016

Paul D. Feigin
Paul D. Feigin*
Affiliation:
Technion — Israel Institute of Technology
*
∗ Postal address: Faculty of Industrial and Management Engineering, Technion — Israel Institute of Technology, Haifa, Israel.
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Abstract

Consider the maximum likelihood estimation of θ based on continuous observation of the process X, which satisfies dXt = θXtdt + dWt . Feigin (1976) showed that, when suitably normalized, the maximum likelihood estimate is asymptotically normally distributed when the true value of θ ≠ 0. The claim that this asymptotic normality also holds for θ = 0 is shown to be false. The parallel discrete-time model is mentioned and the ramifications of these singularities to martingale central limit theory is discussed.

Keywords

MAXIMUM LIKELIHOOD ESTIMATIONORNSTEIN-UHLENBECK PROCESSMARTINGALE CENTRAL LIMIT THEORY

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 16 , Issue 2 , June 1979 , pp. 440 - 444
Copyright
Copyright © Applied Probability Trust 1979 

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References

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