A test for randomness of the environments in a branching process Authors Mohan Kale Department of Statistics University of Pune T. V. Ramanathan Department of Statistics University of Pune Articles

Received: 04 August 1995 Revised: 25 July 1996 DOI :
10.1007/BF02925997

Cite this article as: Kale, M. & Ramanathan, T.V. Statistical Papers (1997) 38: 409. doi:10.1007/BF02925997
Abstract
This paper discusses an approximate score test for testing randomness of environments in a branching process without observing the environments. Using an appropriate martingale central limit theorem the asymptotic null distribution of test statistic is shown to be normal. When the offspring distribution is Poisson, the detail derivation of asymptotic distribution of the test statistic is presented.

Key words
Random environments
branching process
Martingale central limit theorem
score test

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