Estimation of the ratio of a geometric process

Alicja Jokiel-Rokita¹ ; Rafał Topolnicki¹

¹ Faculty of Pure and Applied Mathematics Wrocław University of Science and Technology Wybrzeże Wyspiańskiego 27 50-370 Wrocław, Poland

Applicationes Mathematicae, Tome 44 (2017) no. 1, pp. 105-121

Résumé

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.

Détail

DOI : 10.4064/am2316-12-2016

Keywords: propose estimators ratio parameter geometric process stochastic process ldots which there exists nbsp positive real number called ratio parameter i ldots forms renewal process assume nbsp cumulative distribution function nbsp random variables ldots completely unknown compare accuracy proposed estimators ratio known estimators given lam chan maximum likelihood estimators derived under assumption has known form