Estimation of the ratio of a geometric process
Volume 44 / 2017
Applicationes Mathematicae 44 (2017), 105-121
MSC: Primary 62F10; Secondary 62G05.
DOI: 10.4064/am2316-12-2016
Published online: 3 March 2017
Abstract
We propose some estimators of the ratio parameter of a geometric process, i.e. of a stochastic process $\{X_{i},i=1,2,\ldots \}$ for which there exists a positive real number $a,$ called the ratio parameter, such that $\{Y_{i}=a^{i-1}X_{i},\,i=1,2,\ldots \}$ forms a renewal process. We assume that the cumulative distribution function $F$ of the random variables $Y_{i},$ $i=1,2, \ldots ,$ is completely unknown. We compare the accuracy of the proposed estimators of the ratio with known estimators given by Lam (1992) and by Chan et al. (2006), and also with the maximum likelihood estimators derived under the assumption that $F$ has a known form.
