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標題: 具群體變異數且為一般自回溯相關共變異數結構之成 長曲線分析
Analysis of the growth curve model with grouping variances in general antedependence structure
作者: 郭于銓
Kuo, Yu-Chuan
關鍵字: Maximum likelihood estimates;最大概似估計法;Nonstationary;Predictions;Structured antedependence;非定態;預測;結構性自回溯相關
出版社: 應用數學系所
引用: References [1] Altman, N. S. and Casella, G. (1995). Nonparametric emprical bayes growth curve analysis. Journal of American Statistical Association,90(430):508-515. [2] Frean, T. (1975). A bayesian approach to growth curves. it Biometrika, 62:89- 100. [3] Gabriel, K.R. (1962). Ante-dependence analysis of an ordered set of variabels. Annals of Mathematical Statistics 33,201-212. [4] Geisser, S. (1970). Bayesian analysis of growth curves. Sankhya Ser A, 32:53-64. [5] Geisser, S. (1980). Growth curve analysis. In Krishnaiah, P. R., editor, Handbook of Statistics, volume 1, pages 89-115. North-Holland, Amsterdam. [6] Geisser, S. (1981). Sample reuse procedures for prediction of the unobserved portion of a partially observed vector. Biometrika, 98:243-250. [7] Jennrich, R. I. and Schluchter, M. D. (1986). Unbalanced repeated-measures models with structured covariance matrices. Biometrics, 42:805-820. [8] Keramidas, E. M. and Lee, J. C., 1990: Forecasting technological substitutions with concurrent short time series. Journal of the American Statistical Association 85, 625-632. [9] Kenward, M. G. (1987). A method for comparing profiles of repeated measurements. Applied Statistics, 36:296-308. [10] Lee, J. C. and Geisser, S. (1972). Growth curve prediction. Sankyha Ser.A, 34:393-412. [11] Lee, J. C. and Geisser, S. (1975). Applications of growth curve prediction. Sankyha Ser.A, 37:239-256. [12] Lee, J. C. (1982). Classification of growth curves. In Krishnaiah, P. R. and Kanal, I. W., editors, Handbook of Statistics, volume 2, pages 121-137. North- Holland, Amsterdam. [13] Lee, J. C. (1988). Prediction and estimation of growth curve with special covariance structures. Jounrnal of American Statistical Association, 83:432- 440. [14] Lee, J. C. (1991). Test and model selection for the general growth curve model. Biometrics, 47:147-159. [15] Lee, J. C. and Geisser, S. (1996). On the prediction of growth curves. In Lee, J. C., Zellner, A., and Johnson, W. O., editors, Modelling and Prediction Honoring Seymour Geisser, pages 71-103. Springer, Berlin. [16] Lee, J. C. and Hsu, Y. L. (1997). Bayesian analysis of growth curves with AR(1) dependence. Jounral of Statistical Planning and Inference, 64:205-229. [17] Lee, J. C., Chen, D. T., Hung, H. N. and Chen, J. J., 1999: Analysis of Drug Dissolution. Statistics in Medicine 18, 799-814. [18] Lee, J. C. and Hsu, Y. L. (2003). Estimation and prediction of generalized growth curve with grouping variances in AR(q) dependence structure. Biometrical 45:165-181. [19] Mohsen Pourahmadi. (1999). Joint mean-covariance models with applications to longitudinal data: unconstrained parameterisation Biometrika, 86:677-690. [20] Newton, H. J. (1988). TIMESLAB: A time series analysis laboratory. Pacific Grove, CA: Wadsworth & Brooks/Cole. [21] Potthoff, R. F. and Roy, S. N. (1964). A generalized multivariate analysis of variance model useful especially for growth curve problems. Biometrika, 51:313-326. [22] Rao, C. R. (1987). Prediction of future observations in growth curve models. Statistical Science, 2:434-471. [23] Williams, J. S. and Izenman, A. J. (1981). A class of linear spectral models and analyses for the study of longitudinal data. Technical report, Dept. of Statistics, Colorado State University. [24] Wolfinger, R. D. (1996). Heterogeneous variance-covariance structures for repeated measures. Journal of Agricultural, Biological, and Environmental Statistics 1,205-230. [25] Zimmerman, D. L. and Núñez-Antón on, V. (1997). Structured antedependence models for longitudinal data. In Modelling Longitudinal and Spatially Correlated Data. Methods, Applications, and Future Directions, T. G. Gregoire, D.R. Brillinger, P.J. Diggle, E. Russek-Cohen, W. G.Warren, and R.Wolfinger (eds), 63-76. New York: Springer-Verlag. [26] Zimmerman, D. L. and Núñez-Antón on, V. (2000). Modeling nonstationary longitudinal data. Biometrics, 56:699-705. [27] Zimmerman, D. L. and Núñez-Antón on, V. (2001). Parametric modelling of growth curve data: An overview. Test, 10(1):1-73. (with discussion).
慮下共變異數矩陣可以表示為Σ=DσCDσ , 其中C 為非定態 s 階結構性
的自回溯過程之相關係數矩陣, s < p 而Dσ 為一對角矩陣其中 p 個元素被
分成g(≦ p) 群, 即, Dσ 是﹛σ1 ,…, σg ﹜的函數且σℓ, ℓ= 1,…, g 是
未知。我們亦考慮在此結構下的參數估計和預測, 並以真實資料來說明預測結

In this thesis we consider maximum likelihood analysis of generalized growth
curve model with the Box-Cox transformation when the covariance matrix has
SAD(s) dependence structure with grouping variances. The covariance matrix under
consideration is Σ=DσCDσ where C is the correlation matrix with nonstationary
structured antedependence process of order s, s < p and Dσ is a diagonal matrix
with p elements divided into g(≦p) groups, i.e., Dσ is a function of ﹛σ1,…,σg﹜
and σℓ, ℓ= 1,…, g , are unknown. We consider both parameter estimation and
prediction of future values. Results are illustrated with real data.
其他識別: U0005-0208200714083100
Appears in Collections:應用數學系所

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