The Annals of Statistics

Maximum Likelihood Estimation in the Birth-and-Death Process

Niels Keiding

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Abstract

Maximum likelihood estimation of the parameters $\lambda$ and $\mu$ of a simple (linear) birth-and-death process observed continuously over a fixed time interval is studied. Asymptotic distributions for large initial populations and for large periods of observation are derived and some nonstandard results appear. The result problem of estimation from the discrete skeleton of the process is also discussed.

Article information

Source
Ann. Statist., Volume 3, Number 2 (1975), 363-372.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176343062

Digital Object Identifier
doi:10.1214/aos/1176343062

Mathematical Reviews number (MathSciNet)
MR362773

Zentralblatt MATH identifier
0302.62043

JSTOR
links.jstor.org

Subjects
Primary: 62F10: Point estimation
Secondary: 62M05: Markov processes: estimation 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60F05: Central limit and other weak theorems 62B05: Sufficient statistics and fields

Keywords
Birth-and-death process maximum likelihood estimation estimation in Markov processes discrete skeleton of Markov process weak convergence under random change of time

Citation

Keiding, Niels. Maximum Likelihood Estimation in the Birth-and-Death Process. Ann. Statist. 3 (1975), no. 2, 363--372. doi:10.1214/aos/1176343062. https://projecteuclid.org/euclid.aos/1176343062


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Corrections

  • See Correction: Niels Keiding. Note: Correction to "Maximum Likelihood Estimation in the Birth-and-Death Process". Ann. Statist., Volume 6, Number 2 (1978), 472--472.