Non-ergodic martingale estimating functions and related asymptotics
- Authors
- Hwang, S. Y.; Basawa, I. V.; Choi, M. S.; Lee, S. D.
- Issue Date
- 4-May-2014
- Publisher
- TAYLOR & FRANCIS LTD
- Keywords
- non-ergodic process; martingale estimating functions; branching process; asymptotic optimality; explosive autoregressive model; Primary 62M10
- Citation
- STATISTICS, v.48, no.3, pp 487 - 507
- Pages
- 21
- Journal Title
- STATISTICS
- Volume
- 48
- Number
- 3
- Start Page
- 487
- End Page
- 507
- URI
- https://scholarworks.sookmyung.ac.kr/handle/2020.sw.sookmyung/10892
- DOI
- 10.1080/02331888.2012.748772
- ISSN
- 0233-1888
1029-4910
- Abstract
- Well-known estimation methods such as conditional least squares, quasilikelihood and maximum likelihood (ML) can be unified via a single framework of martingale estimating functions (MEFs). Asymptotic distributions of estimates for ergodic processes use constant norm (e.g. square root of the sample size) for asymptotic normality. For certain non-ergodic-type applications, however, such as explosive autoregression and super-critical branching processes, one needs a random norm in order to get normal limit distributions. In this paper, we are concerned with non-ergodic processes and investigate limit distributions for a broad class of MEFs. Asymptotic optimality (within a certain class of non-ergodic MEFs) of the ML estimate is deduced via establishing a convolution theorem using a random norm. Applications to non-ergodic autoregressive processes, generalized autoregressive conditional heteroscedastic-type processes, and super-critical branching processes are discussed. Asymptotic optimality in terms of the maximum random limiting power regarding large sample tests is briefly discussed.
- Files in This Item
- There are no files associated with this item.
- Appears in
Collections - 이과대학 > 통계학과 > 1. Journal Articles
Items in ScholarWorks are protected by copyright, with all rights reserved, unless otherwise indicated.