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Some convergence theorems on a supercritical Galton-Watson process

Authors:	P. Koteeswaran K. Nanthi K. Suresh Chandra

Affiliation:	(1) University of Madras, Madras;(2) Presidency College, Madras

Abstract:	Summary LetX=(X _n; n≧0,X ₀=1) be a supercritical Galton-Watson process. The limiting distribution of $left( {left( {sumlimits_{n = 0}^N {X_n } } right)^{{{ - 1} mathord{left/ {vphantom {{ - 1} 2}} right. kern-nulldelimiterspace} 2}} left( {sumlimits_{n = 0}^N {X_{n + r} } - hat m^r sumlimits_{n = 0}^N {X_n } } right);r = 2,3, ldots ,T} right)$ ) where is the m.l.e. of the offspring mean, is derived. As an application of this result, some limit theorems leading ultimately to a parameter free result of statistical interest, are also established.

Keywords:	Supercritical Galton-Watson process asymptotic goodness of fit tests
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