Browse > Article
http://dx.doi.org/10.7465/jkdi.2014.25.5.1137

Contemporary review on the bifurcating autoregressive models : Overview and perspectives  

Hwang, S.Y. (Department of Statistics, Sookmyung Women's University)
Publication Information
Journal of the Korean Data and Information Science Society / v.25, no.5, 2014 , pp. 1137-1149 More about this Journal
Abstract
Since the bifurcating autoregressive (BAR) model was developed by Cowan and Staudte (1986) to analyze cell lineage data, a lot of research has been directed to BAR and its generalizations. Based mainly on the author's works, this paper is concerned with a contemporary review on the BAR in terms of an overview and perspectives. Specifically, bifurcating structure is extended to multi-cast tree and to branching tree structure. The AR(1) time series model of Cowan and Staudte (1986) is generalized to tree structured random processes. Branching correlations between individuals sharing the same parent are introduced and discussed. Various methods for estimating parameters and related asymptotics are also reviewed. Consequently, the paper aims to give a contemporary overview on the BAR model, providing some perspectives to the future works in this area.
Keywords
Bifurcating autoregression; branching correlation; branching tree; estimating function; multi-cast model;
Citations & Related Records
Times Cited By KSCI : 4  (Citation Analysis)
연도 인용수 순위
1 Hwang, S. Y. and Basawa, I. V. (2014). Martingale estimating functions for stochastic processes : A review toward a unifying tool. In Contemporary Developments in Statistical Theory, edited by S. Lahiri et al., Springer, Switzerland, 9-28.
2 Hwang, S. Y., Basawa, I. V., Choi, M. S. and Lee, S. D. (2014a). Non-ergodic martingale estimating functions and related asymptotics. Statistics, 48, 487-507.   DOI   ScienceOn
3 Hwang, S. Y., Choi, M. S. and Yeo, In-kwon (2014b). Quasilikelihood and quasi maximum likelihood for GARCH-type processes : Estimating function approach. Journal of the Korean Statistical Society, DOI:10.1016/j.jkss.2014.01.005.   DOI   ScienceOn
4 Hwang, S. Y. and Choi, M. S. (2009). Modeling and large sample estimation for multi-casting autoregression. Statistics & Probability Letters, 79, 1943-1950.   DOI   ScienceOn
5 Hwang, S. Y. and Choi, M. S. (2011). Preliminary identification of branching heteroscedasticity for tree indexed autoregressive processes. Communications of the Korean Statistical Society, 18, 809-816.   과학기술학회마을   DOI   ScienceOn
6 Hwang, S. Y. and Kang, K. H. (2012). Asymptotics for a class of generalized multicast autoregressive process. Journal of the Korean Statistical Society, 41, 543-554.   DOI   ScienceOn
7 Lee, H. Y. (2012). Property of regression estimators in GEE models for ordinal reponses, Journal of the Korean Data & Information Science Society, 23, 209-218.   DOI   ScienceOn
8 Mao. M. (2014). The asymptotic behaviors for least square estimation of multicast autoregressive processes. Journal of Multivariate Analysis, 129, 110-124   DOI   ScienceOn
9 Straumann, D. and Mikosch, T. (2006). Quasi-maximum-likelihood estimation in conditionally heteroscedastic time series : A stochastic recurrence equations approach. Annals of Statistics, 34, 2449-2495.   DOI
10 Baek, J. S., Choi, M. S. and Hwang, S. Y. (2012). A broad class of partially specified autoregressions on multicasting data. Communications in Statistics - Theory and Methods, 41, 178-193.   DOI
11 Basawa, I. V. and Zhou, J. (2004). Non-Gaussian bifurcating models and quasi likelihood estimation. Journal of Applied Probability, 41A, 55-64.   DOI
12 Cowan R. and Staudte, R. G. (1986). The bifurcating autoregression model in cell lineage studies. Biometrics, 42, 769-783.   DOI   ScienceOn
13 Francq, C. and Zakoian, J. M. (2013). Optimal predictions of powers of conditionally heteroscedastic processes. Journal of Royal Statistical Society B, 75, 345-367.   DOI   ScienceOn
14 Godambe, V. P. (1985). The foundation of finite sample estimation in stochastic processes. Biometrika, 72, 419-428.   DOI   ScienceOn
15 Heyde, C. C. (1997). Quasi-likelihood and its application, Springer, New York.
16 Hwang, S. Y. and Basawa, I. V. (2011). Asymptotic optimal inference for multivariate branching-Markov processes via martingale estimating functions and mixed normality. Journal of Multivariate Analysis, 102, 1018-1031.   DOI   ScienceOn
17 Huggins, R. M. and Basawa, I. V. (1999). Extensions of the bifurcating autoregressive model for cell lineage data. Journal of Applied Probability, 36, 1225-1233.   DOI   ScienceOn
18 Hwang, S. Y. (2011). An overview on models for tree-indexed time series. Quantitative Bio-Sciences, 30, 9-11.
19 Hwang, S. Y. and Basawa, I. V. (2009). Branching Markov processes and related asymptotics. Journal of Multivariate Analysis, 100, 1155-1167.   DOI   ScienceOn
20 Hwang, S. Y. and Basawa, I. V. (2011a), Godambe estimating functions and asymptotic optimal inference. Statistics & Probability Letters, 81, 1121-1127.   DOI   ScienceOn
21 Grunwald G. K., Hyndman, R. J., Tedesco, L. and Tweedie, R. L. (2000). Non-Gaussian conditional linear AR(1) models. Australian and New Zealand Journal of Statistics, 42, 479-495.   DOI   ScienceOn