Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/17607
標題: 具自迴歸相依性與條件異質性之成長曲線分析
Analysis of the growth curve model with autoregressive dependence and conditional heteroscedasticity
作者: 廖宮毅
Liao, Gong Yi
關鍵字: growth curve
成長曲線
autoregressive dependence
heteroscedasiticity
Markov Chain Monte Carlo
自迴歸相依性
異質性
馬可夫鏈-蒙地卡羅
出版社: 應用數學系所
引用: Altman, N. S. and Casella, G. (1995). Nonparametric emprical bayes growth curve analysis. Journal of American Statistical Association, 90(430):508-515. Bollerslev, T. (1986). Generalized autoregressive conditional heteroscedasticity. Journal of Econometrics, 31:307-327. Bollerslev, T. (1990). Modelling the coherence in short-run nominal exchange rates: a multivariate generalized ARCH model. The Review of Economics and Statistics, pages 498-505. Bollerslev, T., Engle, R. F., and Wooldridge, J. M. (1988). A captical asset pricing model with time-varying covariance. Journal of Political Economy, 96(1):116-131. Dempster, A. P., Laird, N. M., and Rubin, D. B. (1977). Maximum likelihood from incomplete data via the em algorithm. Journal of the Royal Statistical society B, 39:1-38. (with discussion). Engle, R. F. (1982). Autogressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 50:987-1007. Engle, R. F. and Kroner, K. (1995). Multivariate simultaneous generalized arch. Econometric Theory, 11:122-150. Frean, T. (1975). A bayesian approach to growth curves. Biometrika, 62:89-100. Geisser, S. (1970). Bayesian analysis of growth curves. Sankhya Ser A, 32:53-64. Geisser, S. (1980). Growth curve analysis. In Krishnaiah, P. R., editor, Handbook of Statistics, volume 1, pages 89-115. North-Holland, Amsterdam. Geisser, S. (1981). Sample reuse procedures for prediction of the unobserved portion of a partially observed vector. Biometrika, 98:243-250. Gentle, J. E. (2003). Random Number Generation and Monte Carlo Methods. Sprigner, second edition. Grizzle, J. E. and Allen, D. M. (1969). Analysis of growth and dose response curves. Biometrics, 25:357-381. Hackera, R. S. and Hatemi-J, A. (2005). A test for multivariate ARCH effects. Applied Economic Letters, 12:411-417. Hasting, W. K. (1970). Monte carlo sampling methods using markov chains and their applications. Biometrika, 57:97-109. Heck, D. L. (1960). Charts of some upper percentage points of the dsitribution of the largest characterictic root. Annals of Mathematical Statistics, 31:625-642. 40 Jennrich, R. I. and Schluchter, M. D. (1986). Unbalanced repeated-measures models with structured covariance matrices. Biometrics, 42:805-820. Kenward, M. G. (1987). A method for comparing profiles of repeated measurements. Applied Statistics, 36:296-308. Khatri, C. G. (1970). A note on a manova model appiled to problems in growth curves. Annals of Institute of Statistical Mathematics, 32:53-64. Khatri, C. G. (1973). Testing some covariance structures under a growth curve model. Journal of Multvariate Analysis, 3:102-116. 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. Lee, J. C. (1988). Prediction and estimation of growth curve with special covariance structures. Jounrnal of American Statistical Association, 83:432-440. Lee, J. C. (1991). Test and model selection for the general growth curve model. Biometrics, 47:147-159. Lee, J. C. and Geisser, S. (1972). Growth curve prediction. Sankyha Ser.A, 34:393- 412. Lee, J. C. and Geisser, S. (1975). Applications of growth curve prediction. Sankyha Ser.A, 37:239-256. 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. 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. Lee, J. C. and Tan, W. Y. (1984). On the degree of polynomial in general linear model. Communications in Statistics Part A - Theory and Methods, 13:781-790. Meng, X. L. and Rubin, D. B. (1993). Maximum likelihood estimation via the ecm algorithm: A general framework. Biometrika, 80:267-278. Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., and Teller, E. (1953). Equations of state calculation by fast computing machines. Journal of Chemical Physics, 21:1087-1092. 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. Rao, C. R. (1965). The theory of the least squares when the parameters are stochastic and its application to the analysis of growth curves. Biometrika, 52:447-458. 41 Rao, C. R. (1966). Covariance adjustment and related problems in multivariate analysis. In Krishnaiah, P. R., editor, Multivariate Analysis, volume 1, pages 87-103. Academic Press, New York. Rao, C. R. (1967). Least squares theory using an estimated dispersion matrix and its application to measurement of signals. In LeCam, L. M. and Neyman, J., editors, Proc. 5th Berkeley Symp. Mathematical Statistics and Probability, volume 1, pages 355-372. University of California Press, Berkeley. Rao, C. R. (1975). Simultaneous estimation of parameters in different linear models and applications to biometric problmes. Biometrics, 31:545-554. Rao, C. R. (1977). Prediction of future observations with soecial reference to linear models. In Krishnaiah, P. R., editor, Multivariate Analysis, volume 4, pages 193- 128. Academic Press, New York. Rao, C. R. (1984). Predition of future observations in polynomial growth curve models. In Proc. Indian Statistical Institute Golden Jubilee Conference on Statis- tics: Applications and New Directions, pages 512-520, Calcutta. Indian Statistical Institute. Rao, C. R. (1987). Prediction of future observations in growth curve models. Sta- tistical Science, 2:434-471. Reinsel, G. (1982). Multivariate repeated-measurement of growth curve models with multivariate random-effects covariance structure. Journal of American Statistical Association, 77:190-195. Reinsel, G. (1984). Estimation and prediction in a multivariate random effects generalized linear model. Journal of American Statistical Association, 79:406- 414. Tsay, R. S. (2002). Analysis of Financial Time Series. John Wiley & Sons. 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. Zimmerman, D. L. and N´nez-Ant´n, V. (2001). Parametric modelling of growth curve data: An overview. Test, 10(1):1-73. (with discussion). 42
摘要: 本文之趣旨為討論具一次自迴歸相依性及一次條件異質性之成長曲線分析.在此假設下所得之多變量常態分佈的概似度函數及其數學性質詳述文中. 作者亦考量了從最大概似估計法觀點及貝氏估計觀點所引導之不同的參數估計法及預測法,在考量最大概似度估計參數時,作者給出了一數值演算方法以求得參數數值解,在考量貝氏估計時,作者使用了馬可夫鏈-蒙地卡羅法以求參數的事後分佈. 作者文中提供了具趣旨所揭之假設條件下的條件估計式及擴充估計式並以實務資料與模擬資料以說明此一成長曲線模式於參數估計與預測觀測值上之表現與效益
The growth curve model that the covariance matrix constructed with autoregressive (AR) dependence of degree 1 and autoregressive conditional heteroscedasiticity (ARCH) of degree 1 is studied in the thesis. The specification of the multivariate normal distribution with these two properties is dedicated. I consider both maximum likelihood inference perspective and Bayesian inference perspective for estimation and prediction. An algorithm is introduced for determining maximum likelihood estimates of the unknown parameters, on the other hand, Markov Chain Monte Carlo methods are elaborated for Bayesian estimation and prediction. The forms of the condictional predictor and extended predictor are provided and illustrated with numerical results of both real data and simulated data
URI: http://hdl.handle.net/11455/17607
其他識別: U0005-2306200614190000
文章連結: http://www.airitilibrary.com/Publication/alDetailedMesh1?DocID=U0005-2306200614190000
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