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Local asymptotic normality for bifurcating autoregressive processes and related asymptotic inference
- Authors
- Hwang S.Y.; Basawa I.V.; Yeo I.K.
- Issue Date
- Jan-2009
- Keywords
- Bifurcating model; LAN; Martingale array; Maximum likelihood; Score test
- Citation
- Statistical Methodology, v.6, no.1, pp 61 - 69
- Pages
- 9
- Journal Title
- Statistical Methodology
- Volume
- 6
- Number
- 1
- Start Page
- 61
- End Page
- 69
- ISSN
- 1572-3127
- Abstract
- This article is concerned with the local asymptotic normality (LAN) of the log-likelihood for the bifurcating autoregressive model (BAR) for tree structured data where each individual in one generation gives rise to two off-spring in the next generation. We derive the LAN property for the pth-order BAR model. Asymptotic optimal inference for the model parameters can be deduced as a consequence of LAN. In particular, an efficient score test is derived as an application. A simulation study is conducted to address the issue regarding how many generations are required for asymptotic results to be useful in practice. © 2008 Elsevier B.V. All rights reserved.
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