A study of the behaviour of certain known estimators on the non-extinction path of a branching process

Abstract

Consider a super-critical Galton--Watson branching process. Gadag and Kunte (1980) have shown that such a process when restricted to non-extinction set does not retain branching property. In this note, we study the properties of the known estimators of the offspring mean (Nagaev, 1967) and offspring probability distribution and offspring probability generating function (Pakes, 1975), in the light of the result of Gadag and Kunte (1980).