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Some characterizations of non-ergodic estimating functions for stochastic processes

Authors
Hwang, S. Y.
Issue Date
Dec-2015
Publisher
KOREAN STATISTICAL SOC
Keywords
Estimating function (EF); Non-ergodic EF; Random norm; Score
Citation
JOURNAL OF THE KOREAN STATISTICAL SOCIETY, v.44, no.4, pp 661 - 667
Pages
7
Journal Title
JOURNAL OF THE KOREAN STATISTICAL SOCIETY
Volume
44
Number
4
Start Page
661
End Page
667
URI
https://scholarworks.sookmyung.ac.kr/handle/2020.sw.sookmyung/10149
DOI
10.1016/j.jkss.2015.06.003
ISSN
1226-3192
1876-4231
Abstract
We are concerned with the stochastic process for which the likelihood of the data, although it does exist, is possibly unknown to us. In order to estimate parameter, we are led to appropriate estimating functions (EF, for short) including the (quasi) maximum likelihood score. A formal definition of the general non-ergodic estimating function is made in this paper. This can be viewed as a generalization of the non-ergodic maximum likelihood score (due to Basawa and Koul (1979), and Basawa and Scott (1983)) toward the theory of EFs. In addition, some characterizations on the non-ergodic EFs are made. It is interesting to note non-standard cases where non-stationary process may yield an ergodic EF while stationary process can produce a non-ergodic EF. Various examples are presented to illustrate the main results. (C) 2015 The Korean Statistical Society. Published by Elsevier B.V. All rights reserved.
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