## The Annals of Statistics

### Estimation of the Means in the Branching Process with Immigration

#### 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

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