The limit distribution of a Markov chain of order k > 1 is obtained under conditions weaker than those assumed by Raftery (1985). The results are shown to be valid also for arbitrary state space Markov sequences of order k > 1. XES such that n(y) > 0, L n(y) = 1. yES t
Let X be a random variable having an exponential distribution with unknown mean 8. Further, it is assumed that prior knowledge about 8 is available in the form of an initial estimate 80 of 8.It is proposed to estimate 8 by a testimator 9 that is based upon the result of a test of the hypothesis Ho: 8 = 80. If Ho is accepted based on the first sample of size nl we take 6 = Sl t (1 -R)80 where the weighting factor R is a function of the test statistic for testing Ho. However, if Ho is rejected we obtain a second sample of size n2, and take 6 = (nlX1 + n2X2)/(nl + n2). Choosing the weighing factor L appropriately, an expression for the mean squared error of 6 is derived and comparisons are made with the variance of a single sample mean. Also an expression for the bias of 6 is derived.
This paper establishes the strong consistency of the maximum likelihood estimators of the parameters of discrete- and continuous-time Markov branching processes with immigration. The asymptotic distributions of the maximum likelihood estimators of the parameters of a Galton–Watson branching process with immigration are also obtained.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.