Efficient sequential estimation in a markov branching process with immigration
Titel:
Efficient sequential estimation in a markov branching process with immigration
Auteur:
Jang, J.S. Bai, D.S.
Verschenen in:
Communications in statistics
Paginering:
Jaargang 15 (1986) nr. 5 pagina's 1681-1697
Jaar:
1986
Inhoud:
Sequential estimation of parameters In a continuous time Markov branching process with Immigration with split rate λ1 Immigration rate λ2, offspring distribution {p1j≥O) and Immigration distribution {p2j≥l} is considered. A sequential version of the Cramer-Rao type information inequality is derived which gives a lower bound on the variances of unbiased estimators for any function of these parameters. Attaining the lower bounds depends on whether the sampling plan or stopping rule S, the estimator f, and the parametric function g = E(f) are efficient. All efficient triples (S,f,g) are characterized; It Is shown that for i = 1,2, only linear combinations of λipijj's or their ratios are efficiently estimable. Applications to a Yule process, a linear birth and death process with immigration and an M/M/∞ queue are also considered
Tijdschrift beschrijving