The Annals of Statistics

Estimation of the Means in the Branching Process with Immigration

C. Z. Wei and J. Winnicki

Full-text: Open access

Abstract

Let $\{X_n\}$ be the branching process with immigration and let $m$ and $\lambda$ be the means of the offspring and immigration distributions, respectively. Estimation results for $m$ and $\lambda$ were obtained in the literature for the subcritical $(m < 1)$ and supercritical $(m > 1)$ cases, but no unified estimation procedure was developed, which would allow inference without knowledge of the range of $m$. The goal of this paper is to investigate this problem.

Article information

Source
Ann. Statist., Volume 18, Number 4 (1990), 1757-1773.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176347876

Digital Object Identifier
doi:10.1214/aos/1176347876

Mathematical Reviews number (MathSciNet)
MR1074433

Zentralblatt MATH identifier
0736.62071

JSTOR
links.jstor.org

Subjects
Primary: 62M99: None of the above, but in this section
Secondary: 62M05: Markov processes: estimation

Keywords
Branching process with immigration conditional least squares weighted conditional least squares inconsistency limiting distribution

Citation

Wei, C. Z.; Winnicki, J. Estimation of the Means in the Branching Process with Immigration. Ann. Statist. 18 (1990), no. 4, 1757--1773. doi:10.1214/aos/1176347876. https://projecteuclid.org/euclid.aos/1176347876


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