Communications for Statistical Applications and Methods

  • 제18권6호
  • /
  • Pages.809-816
  • /
  • 2011
  • /
  • 2287-7843(pISSN)
  • /
  • 2383-4757(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지
DOI QR코드

DOI QR Code

Preliminary Identification of Branching-Heteroscedasticity for Tree-Indexed Autoregressive Processes

  • Hwang, S.Y. (Department of Statistics, Sookmyung Women's University) ;
  • Choi, M.S. (Department of Statistics, Sookmyung Women's University)
  • 투고 : 20110700
  • 심사 : 20110900
  • 발행 : 2011.11.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

A tree-indexed autoregressive(AR) process is a time series defined on a tree which is generated by a branching process and/or a deterministic splitting mechanism. This short article is concerned with conditional heteroscedastic structure of the tree-indexed AR models. It has been usual in the literature to analyze conditional mean structure (rather than conditional variance) of tree-indexed AR models. This article pursues to identify quadratic conditional heteroscedasticity inherent in various tree-indexed AR models in a unified way, and thus providing some perspectives to the future works in this area. The identical conditional variance of sisters sharing the same mother will be referred to as the branching heteroscedasticity(BH, for short). A quasilikelihood but preliminary estimation of the quadratic BH is discussed and relevant limit distributions are derived.

키워드

참고문헌

  1. Baek, J. S., Choi, M. S. and Hwang, S. Y. (2011). A broad class of partially specified autoregressions on multicasting data, Communications in Statistics-Theory and Methods, to appear.
  2. Basawa, I. V. and Zhou, J. (2004). Non-Gaussian bifurcating models and quasi-likelihood estimation, Journal of Applied Probability, Spec. 41A, 55-64.
  3. Cowan, R. and Staudte, R. G. (1986). The bifurcating autoregression model in cell lineage studies, Biomertics, 42, 769-783. https://doi.org/10.2307/2530692
  4. Godambe, V. P. (1985). The foundation of finite sample estimation in stochastic processes, Biometrika, 72, 419-428. https://doi.org/10.1093/biomet/72.2.419
  5. Grunwald, G. K., Hyndman, R. J., Tedesco, L. and Tweedie, R. L. (2000). Non-Gaussian conditional linear AR(1) models, Australian & New Zealand Journal of Statistics, 42, 479-495. https://doi.org/10.1111/1467-842X.00143
  6. Hwang, S. Y. (2011). An overview on models for tree-indexed time series, Quantitative Bio-Sciences, 30, 9-11.
  7. 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. https://doi.org/10.1016/j.jmva.2011.02.002
  8. Hwang, S. Y. and Choi, M. S. (2009). Modeling and large sample estimatin for multi-casting autoregression, Statistics & Probability Letters, 79, 1943-1950. https://doi.org/10.1016/j.spl.2009.06.005

피인용 문헌

  1. Contemporary review on the bifurcating autoregressive models : Overview and perspectives vol.25, pp.5, 2014, https://doi.org/10.7465/jkdi.2014.25.5.1137