Confidence intervals based on the deviance statistic for the hyperparameters in state space models

References

• Barndorff-Nielsen, O. 1986. Inference on full or partial parameters based on the standardized signed log likelihood ratio. Biometrika 73:307–22.
   Google Scholar
• Brazzale, A. R., A. C. Davison, and N. Reid. 2007. Applied asymptotics: Case studies in small-sample statistics, Vol. 23. Cambridge: Cambridge University Press.
   Google Scholar
• Cavanaugh, J., and R. Shumway. 1996. On computing the expected Fisher information matrix for state-space model parameters. Statistics & Probability Letters 26:347–55.
   Google Scholar
• Chen, J., and R. I. Jennrich. 1996. The signed root deviance profile and confidence intervals in maximum likelihood analysis. Journal of the American Statistical Association 91:993–8.
   Google Scholar
• Cormen, T. H., C. E. Leiserson, and R. L. Rivest. 1990. Introduction to algorithms. Cambridge: MIT Press and McGraw-Hill.
   Google Scholar
• Doornik, J. A. 2006. Object-oriented matrix programming using Ox. 5th ed. London: Timberlake Consultants Press.
   Google Scholar
• Dowell, M., and P. Jarrat. 1972. The pegasus method for computing the root of an equation. BIT Numerical Mathematics 12:503–8.
   Google Scholar
• Dukic, V., H. F. Lopes, and N. G. Polson. 2012. Tracking epidemics with Google flu trends data and a state-space SEIR model. Journal of the American Statistical Association 107 (500):1410–26.
   Google Scholar
• Efron, B. 1979. Bootstrap methods: Another look at the jackknife. The Annals of Statistics 7:1–26.
   Google Scholar
• Efron, B., and R. Tibshirani. 1993. An introduction to the bootstrap. London: Chapman & Hall.
   Google Scholar
• Franco, G. C., T. R. Santos, J. A. Ribeiro, and F. R. B. Cruz. 2008. Confidence intervals for the hyperparameters in structural models. Communications in Statistics 37:486–97.
   Google Scholar
• Gimenez, O., R. Choquet, L. Lamor, P. Scofield, D. Fletcher, J. Lebreton, and R. Pradel. 2005. Efficient profile likelihood confidence intervals for capture-recapture model. Journal of Agricultural, Biological and Environmental Statistic 10:184–96.
   Google Scholar
• Hamilton, J. D. 1994. State-space models. In: Handbook of Econometrics, ed. R. F. Engle and D. L. McFadden, Vol. IV. 3039–80. Amsterdam: Elsevier Science B.V, Chap. 50.
   Google Scholar
• Harvey, A. C. 1989. Forecasting, structural time series models and the Kalman filter. Cambridge: University Press.
   Google Scholar
• Heinze, G., and M. Chemper. 2002. A solution to the problem of separation in logistic regression. Statistics in Medicine 21:2409–19.
   Google Scholar
• Kalman, R. E. 1960. A new approach to linear filtering and prediction problems. Trans. ASME J. Basic Eng. 82:35–45.
   Google Scholar
• Koopman, S., N. Shephard, and J. Doornik. 1999. Statistical algorithms for models in state space form using SsfPack 2.2. Econometrics Journal 2:107–60.
   Google Scholar
• Neale, M. C., and M. B. Miller. 1997. The use of likelihood based confidence intervals in genetic models. Behavior Genetics 27:113–20.
   Google Scholar
• Nobre, A. A., A. Schmidt, and H. F. Lopes. 2005. Spatio-temporal models for mapping the incidence of malaria in Pará. Environmetrics 16 (3):291–304.
   Google Scholar
• Pfanzagl, J. 1994. Parametric statistical theory with the assistance of R. Berlin: Walter de Gruyter.
   Google Scholar
• Pfefferman, D., and R. Tiller. 2005. Bootstrap approximation to predictions MSE for state-space models with estimated parameters. Journal of Time Series Analysis 26:893–916.
   Google Scholar
• Quenneville, B., and A. Singh. 2000. Bayesian prediction mean squared error for state space models with estimated parameters. Journal of Time Series Analysis 21:219–36.
   Google Scholar
• Rodriguez, A., and E. Ruiz. 2009. Bootstrap prediction intervals in state space models. Journal of Time Series Analysis 30:167–78.
   Google Scholar
• Rodriguez, A., and E. Ruiz. 2012. Bootstrap prediction mean squared errors of unobserved states based on the Kalman filter with estimated parameters. Computational Statistics and Data Analysis 56:62–74.
   Google Scholar
• Rolke, W. A, A. M. López, and J. Conrad. 2005. Limits and confidence intervals in the presence of nuisance parameters. Nucl.Instrum. Methods Phys. Res. A. 551:493–551.
   Google Scholar
• Santos, T. R., G. C. Franco, and D. Gamerman. 2010. Comparison of classical and Bayesian approaches for intervention analysis in structural models. International Statistical Review 78 (2):218–39.
   Google Scholar
• Shanno, D. F. 1970. Conditioning of quasi-Newton methods for function minimization. Mathematics of Computation 24:647–56.
   Google Scholar
• Stoffer, D. S., and K. D. Wall. 1991. Bootstrapping state-space models: Gaussian maximum likelihood estimation and the Kalman filter. Journal of the American Statistical Association 86:1024–33.
   Google Scholar
• Wait, R. 1979. The numerical solution of algebraic equations. Chichester, NY: John Wiley & Sons.
   Google Scholar
• Wilks, S. S. 1938. The large-sample distribution of the likelihood ratio for testing composite hypotheses. The Annals of Mathematical Statistics 9:60.
   Google Scholar