Abstract
We consider the general regression problem for binary time series where the covariates are stochastic and time dependent and the inverse link is any differentiable cumulative distribution function. This means that the popular logistic and probit regression models are special cases. The statistical analysis is carried out via partial likelihood estimation. Under a certain large sample assumption on the covariates, and owing to the fact that the score process is a martingale, the maximum partial likelihood estimator is consistent and asymptotically normal. From this we obtain the asymptotic distribution of a certain useful goodness of fit statistic.
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References
Agresti, A. (1990). Categorical Data Analysis. Wiley, New York.
Andersen, P. K. and R. D. Gill. (1982). Cox’s regression model for counting processes: A large sample study. Annals of Statistics, 10, 1100–1120.
Cox, D. R. (1970). The Analysis of Binary Data. Methuen, London.
Cox, D. R. (1975). Partial likelihood. Biometrika, 62, 69–76.
Diggle, P. J., K-Y. Liang, and S. L. Zeger. (1994). Analysis of Longitudinal Data. Oxford University Press, Oxford.
Fahrmeir, L. and H. Kaufmann. (1987). Regression models for nonstationary categorical time series. Journal of Time Series Analysis, 8, 147–160.
Fahrmeir, L. and G. Tutz. (1994). Multivariate Statistical Modelling Based on Generalized Linear Models. Springer, New York.
Fokianos, K. (1996). Categorical Time Series: Prediction and Control. Ph.D. Thesis, Department of Mathematics, University of Maryland, College Park.
Fokianos, K. and B. Kedem. (1998). Prediction and Classification of nonstationary categorical time series. Journal of Multivariate Analysis, 67, 277–296.
Firth, D (1991). Generalized linear models. Chapter 3 of D. Hinkley et al. eds. (1991). Statistical Theory and Modelling. In Honour of Sir David Cox, FRS, Chapman and Hall, London.
Jacod, J. (1987). Partial likelihood processes and asymptotic normality. Stochastic Processes and their Applications, 26, 47–71.
Kaufmann, H. (1987). Regression models for nonstationary categorical time series: Asymptotic estimation theory. Annals of Statistics, 15, 79–98.
Kedem, B. (1980). Binary Time Series. Dekker, New York.
Keenan, D. M. (1982). A time series analysis of binary data. Journal of the American Statistical Association, 77, 816–821.
McCullagh, P. and J. A. Nelder. (1989). Generalized Linear Models, 2nd ed. Chapman and Hall, London.
McCullagh, P. (1980). Regression models for ordinal data (with discussion). Journal of the Royal Statistical Society, B, 42, 109–142.
Rao, C. R. (1973). Linear Statistical Inference and its Applications, 2nd ed. John Wiley, New York.
Schoenfeld, D. (1980). Chi-squared goodness-of-fit for the proportional hazard regression model. Biometrika, 67, 145–153.
Slud, E. (1982). Consistency and efficiency of inferences with the partial likelihood. Biometrika, 69, 547–552.
Slud, E. (1992). Partial likelihood for continuous-time stochastic processes. Scandinavian Journal of Statistics, 19, 97–109.
Slud, E. and B. Kedem. (1994). Partial likelihood analysis of logistic regression and autoregression. Statistica Sinica, 4, 89–106.
Wong, W. H. (1986). Theory of partial likelihood. Annals of Statistics, 14, 88–123.
Zeger, S. L. and B. Qaqish. (1988). Markov regression models for time series: A quasi likelihood approach. Biometrics, 44, 1019–1031.
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Kedem, B., Fokianos, K. (2002). Regression Models for Binary Time Series. In: Dror, M., L’Ecuyer, P., Szidarovszky, F. (eds) Modeling Uncertainty. International Series in Operations Research & Management Science, vol 46. Springer, New York, NY. https://doi.org/10.1007/0-306-48102-2_9
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DOI: https://doi.org/10.1007/0-306-48102-2_9
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