Asymptotic distribution of the CLSE in a critical process with immigration

I. Rahimov

Stochastic Processes and their Applications, 2008, vol. 118, issue 10, 1892-1908

Abstract: It is known that in the critical case the conditional least squares estimator (CLSE) of the offspring mean of a discrete time branching process with immigration is not asymptotically normal. If the offspring variance tends to zero, it is normal with normalization factor n2/3. We study a situation of its asymptotic normality in the case of non-degenerate offspring distribution for the process with time-dependent immigration, whose mean and variance vary regularly with non-negative exponents [alpha] and [beta], respectively. We prove that if [beta] 1+2[alpha], its limit distribution is not normal but can be expressed in terms of the distribution of certain functionals of the time-changed Wiener process. When [beta]=1+2[alpha] the limit distribution depends on the behavior of the slowly varying parts of the mean and variance.

Keywords: Branching; process; Time-dependent; immigration; Functional; Skorokhod; space; Least; squares; estimator (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (2)

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