Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
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THRESHOLD MODELING FOR BIFURCATING AUTOREGRESSION AND LARGE SAMPLE ESTIMATION

  • Hwang, S.Y. (Department of Statistics, Sookmyung Women's University) ;
  • Lee, Sung-Duck (Department of Information & Statistics, Basic Science Research Institute, Chungbuk National University)
  • Published : 2006.12.31
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Abstract

This article is concerned with threshold modeling of the bifurcating autoregressive model (BAR) originally suggested by Cowan and Staudte (1986) for tree structured data of cell lineage study where each individual $(X_t)$ gives rise to two off-spring $(X_{2t},\;X_{2t+1})$ in the next generation. The triplet $(X_t,\;X_{2t},\;X_{2t+1})$ refers to mother-daughter relationship. In this paper we propose a threshold model incorporating the difference of 'fertility' of the mother for the first and second off-springs, and thereby extending BAR to threshold-BAR (TBAR, for short). We derive a sufficient condition of stationarity for the suggested TBAR model. Also various inferential methods such as least squares (LS), maximum likelihood (ML) and quasi-likelihood (QL) methods are discussed and relevant limiting distributions are obtained.

Keywords

References

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