Power divergence family of tests for categorical time series models

Annals of the Institute of Statistical Mathematics

Volumn 54, Issue 3, 2002, Pages 543-564

  Fokianos, Konstantinos ^a  

^a UNIVERSITY OF CYPRUS   (Cyprus)

Author keywords

Logistic regression; Martingale; Multinomial logits; Partial likelihood; Power; Proportional odds; Stochastic time dependent covariates

Indexed keywords

ASYMPTOTIC STABILITY; COMPUTER SIMULATION; CONVERGENCE OF NUMERICAL METHODS; MATHEMATICAL MODELS; MATRIX ALGEBRA; MAXIMUM LIKELIHOOD ESTIMATION; PROBABILITY DISTRIBUTIONS; RANDOM PROCESSES; REGRESSION ANALYSIS; TIME SERIES ANALYSIS; VECTORS;

LOGISTIC REGRESSION; MARTINGALE; MULTINOMIAL LOGITS; PARTIAL LIKELIHOOD; POWER DIVERGENCE; PROPORTIONAL ODDS; STOCHASTIC TIME DEPENDENT COVARIATES;

STATISTICAL TESTS;

EID: 12244283691     PISSN: 00203157     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022459010316     Document Type: Article

References (33)

1. Agresti, A. (1990). Categorical Data Analysis, Wiley, New York.
2. Andersen, P. K. and Gill, R. D. (1982), Cox's regression models for counting process: A large sample approach, Ann. Statist., 10, 1100-1120.
3. Arjas, E. and Haara, P. (1987). A logistic regression model for hazard: Asymptotic results, Scand. J. Statist., 14, 1-18.
4. Bonney, E. G. (1987). Logistic regression for dependent binary observations, Biometrics, 43, 951-973.
5. Brillinger, D. R. (1996). An analysis of ordinal-valued time series, Athens Conference on Applied Probability and Time Series Analysis, Vol. II: Time Series Analysis in Memory of E. J. Hannan, Lecture Notes in Statist., No. 115, 73-87, Springer, New York.
6. Cox, D. R. (1975). Partial likelihood, Biometrika, 62, 69-76.
7. Cressie, N. A. C. and Read, T. R. C. (1984). Multinomial goodness-of-fit tests, J. Roy. Statist. Soc. Ser. B, 46, 440-464.
8. Dale, J. R. (1986). Asymptotic normality of goodness-of-fit statistics for sparse product multinomials, J. Roy. Statist. Soc. Ser. B, 48, 48-59.
9. Fahrmeir, L. and Kaufmann, H. (1987). Regression models for nonstationary categorical time series, J. Time Ser. Anal., 8, 147-160.
10. Fahrmeir, L. and Tutz, G. (1994). Multivariate Statistical Modeling Based on Generalized Linear Models, Springer, New York.
11. Fokianos, K. and Kedem, B. (1998), Prediction and classification of non-stationary categorical time series, J. Multivariate Anal., 67, 277-296.
12. Fokianos, K. and Kedem, B. (1999). A stochastic approximation algorithm for the adaptive control of time series following generalized linear models, J. Time Ser. Anal., 20, 289-308.
13. Gleser, L. J. and Moore, D. S. (1985). The effect of positive dependence on chi-square tests for categorical data, J. Roy. Statist. Soc. Ser. B, 47, 459-465.
14. Hall, P. and Heyde, C. C. (1980). Martingale Limit Theory and Its Applications, Academic Press, New York.
15. Holst, L. (1972). Asymptotic normality and efficiency for certain goodness of fit tests, Biometrika, 59, 137-145.
16. Kaufmann, H. (1987). Regression models for nonstationary categorical time series: Asymptotic estimation theory, Ann. Statist., 15, 79-98.
17. Koehler, K. J. (1986). Goodness-of-fit tests for log-linear models in sparse contingency tables, J. Amer. Statist. Assoc., 81, 483-493.
18. Korn, E. L. and Whittemore, A. S. (1979). Methods for analyzing panel studies of acute health effects of air pollution, Biometrics, 35, 795-802.
19. Li, W. K. (1991). Testing model adequacy for some markov regression models for time series, Biometrika, 78, 83-89.
20. Liang, K.-Y. and Zeger, S. L. (1989). A class of logistic regression models for multivariate binary time series, J. Amer. Statist. Assoc., 84, 447-451.
21. McCullagh, P. (1980). Regression models for ordinal data (with discussion), J. Roy. Statist. Soc. Ser. B, 42, 109-142.
22. McCullagh, P. (1986). The conditional distribution of goodness-of-fit statistics for discrete data, J. Amer. Statist. Assoc., 81, 104-107.
23. McCullagh, P. and Nelder, J. A. (1989). Generalized Linear Models, 2nd ed., Chapman and Hall, London.
24. Morris, C. (1975). Central limit theorem for multinomial sums, Ann. Statist., 3, 165-188.
25. Muenz, L. R. and Rubinstein, L. (1985). Markov models for covariate dependence of binary sequences, Biometrics, 41, 91-101.
26. Osius, G. (1985). Goodness-of-fit tests for binary data with (possible) small expectations but large degrees of freedom, Supplement to Statist. Decisions, 2, 213-224.
27. Osius, G. and Rojek, D. (1992). Normal goodness-of-fit tests for multinomial models with large degrees of freedom, J. Amer. Statist. Assoc., 87, 1145-1152.
28. Read, T. R. C. and Cressie, N. A. C. (1988). Goodness-of-fit Statistics for Discrete Multivariate Data, Springer, New York.
29. Schoenfeld, D. (1980). Chi-square goodness-of-fit test for the proportional hazards regression model, Biometrika, 67, 145-153.
30. Slud, E. and Kedem, B. (1994). Partial likelihood analysis of logistic regression and autoregression, Statist. Sinica, 4, 89-106.
31. Stern, R. D. and Coe, R. (1984). A model fitting analysis of daily rainfall data, J. Roy. Statist. Soc. Ser. A, 147, 1-34.
32. Weiss, L. (1976). The normal approximation to the multinomial with increasing number of classes, Naval Res. Logist. Quarterly, 23, 139-149.
33. Wong, W. H. (1986). Theory of partial likelihood, Ann. Statist., 14, 88-123.