Estimation of smooth time-varying parameters in state space models

Journal of Computational and Graphical Statistics

Volumn 16, Issue 4, 2007, Pages 813-832

  Zhu, Haihong ^a   Wu, Hulin ^a  

^a UNIVERSITY OF ROCHESTER   (United States)

Author keywords

Maximum likelihood estimate; Penalized likelihood; Smoothing spline

Indexed keywords

EID: 38049120250     PISSN: 10618600     EISSN: None     Source Type: Journal    
DOI: 10.1198/106186007X255991     Document Type: Article

References (46)

1. Anderson, R. M., and May, R. M. (1988), "Epidemiology Parameters of HIV Transmission," Nature, 333, 514-519.
2. Ansley, C. F., and Kohn, R. (1985), "Estimation, Filtering and Smoothing in State Space Models with Incompletely Specified Initial Conditions," The Annals of Statistics, 11, 1286-1316.
3. _ (1987), "Efficient Generalized Cross-Validation for State Space Models," Biometrika, 74, 139-148.
4. Atkinson, K. (1978), An Introduction to Numerical Analysis, New York: Wiley.
5. Carlin, B. P., Polson, N. G., and Staffer, D. S. (1992), "A Monte Carlo Approach to Non-normal and Nonlinear State-space Modeling? Journal of the American Statistical Association, 87, 439-500.
6. Ding, A. A., and Wu, H. (2001), "Assessing Antiviral Potency of Anti-HIV Therapies in Vivo by Comparing Viral Decay Rates in Viral Dynamic Models," Biostatistics, 2, 13-29.
7. Eggermont, P., and LaRiccia, V. N. (2001), Maximum Penalized Likelihood Estimation, New York: Springer-Verlag.
8. Essunger, P., and Perelson, A. S. (1994), "Modeling HIV Infection of CD4+ T-cell Subpopulations," Journal of Theoretical Biology, 170, 367-391.
9. Eubank, R. L. (1988), Spline Smoothing and Nonparametric Regression, New York: Marcel Dekker.
10. Eubank, R. L., Huang, C., Muñoz, Y., Wang, N., Wang, S., and Buchanan, R. J. (2004), "Smoothing Spline Estimation in Varying-Coefficient Models," Journal of the Royal of Statistical Society, Ser. B, 66, 653-667.
11. Godsill, S. J., Doucet, A., and West, M. (2004), "Monte Carlo Smoothing for Nonlinear Time Series," Journal of the American Statistical Association, 99, 156-168.
12. Gordon, N. J., Salmond, D. J., and Smith, A. F. M. (1993), "Novel Approach to Nonlinear/Non-Gaussian Bayesian State Estimation," IEEE Proceedings-F, 140, 107-113.
13. Green, P., and Silverman, B. (1994), Nonparametric Regression and Generalized Linear Models, New York: Chapman and Hall.
14. Gu, C. (2002), Smoothing Spline ANOVA Models, New York: Springer-Verlag.
15. Guo, W., Wang, Y., and Brown, M. B. (1999), "A Signal Extraction Approach to Modeling Hormone Time Series with Pulses and a Changing Baseline," Journal of the American Statistical Association, 94, 746-756.
16. Guo, W. (2002), "Functional Mixed Effects Models," Biometrics, 58, 121-128.
17. Harvey, A. (1989), Forecasting. Structural Time Series Models and the Kalman Filter, New York: Cambridge University Press.
18. Hastie, T., and Tibshirani, R. (1990), Generalized Additive Models, London: Chapman and Hall.
19. Ho, D. D., Neumann, A. U., Perelson, A. S., Chen, W., Leonard, J. M., and Markowitz, N. M. (1995), "Rapid Turnover of Plasma Virions and CD4 Lymphocytes in HIV-1 Infection," Nature, 373, 123-126.
20. Huang, Y., Rosenkranz, S. L., and Wu, H. (2003), "Modeling HIV Dynamics and Antiviral Response with Consideration of Time-Varying Drug Exposures, Adherence and Phenotypic Sensitivity," Mathematical Bioscience, 184, 165-186.
21. Huang, Y., Liu, D. and Wu, H. (2006), "Hierarchical Bayesian Methods for Estimation of Parameters in a Longitudinal HIV Dynamic System," Biometrics, 62, 413-423.
22. Huang, Y., and Wu, H. (2006), "A Bayesian Approach for Estimating Antiviral Efficacy in HIV Dynamic Models," Journal of Applied Statistics 33, 155-174.
23. Kimeldorf, G., and Wahba, G. (1971), "Some Results on Tchebycheffian Spline Functions," Journal of Mathematical Analysis and Applications, 33, 82-95.
24. Kitagawa, G. (1993), "Monte Carlo Filter and Smoother for Non-Gaussian Nonlinear State Space Model," Journal of Computational and Graphical Statistics, 5, 1-25.
25. Kohn, R., and Ansley, C. F. (1985), "Efficient Estimation and Prediction in Time Series Regression Models," Biometrika, 72, 694-697.
26. _ (1989), "A Fast Algorithm for Signal Extraction, Influence and Cross-Validation in State Space Models," Biometrika, 76, 65-79.
27. Liu, J. S., and Chen, R. (1998), "Sequential Monte Carlo Methods for Dynamic Systems," Journal of the American Statistical Association, 93, 1032-1044.
28. Merrill, S. (1988), "AIDS: Background and the Dynamics of the Decline of Immunocompetence," in Theoretical Immunology, Part 2, ed. A. S. Perelson, Redwood City, CA: Addison-Wesley.
29. _ (1989), Modeling the Interaction of HIV with the Cells of the Immune System, in Mathematical and Statistical Approaches to AIDS Epidemiology, Lecture Notes in Biomath, 83, New York: Springer-Verlag.
30. Nowak, M. A., and May, R. M. (2000), Virus Dynamics: Mathematical Principles of Immunology and Virology, Oxford: Oxford University Press.
31. Perelson, A. S., Neumann, A. U., Markowitz, M., Leonard, J. M., and Ho, D. D. (1996), "HIV-1 Dynamics in Vivo: Virion Clearance Rate, Infected Cell Life-span, and Viral Generation Time," Science, 271, 1582-1586.
32. Perelson, A. S., Essunger, P., Cao, Y., Vesanen, M., Hurley, A., Saksela, K., Markowitz, M., and Ho, D. D. (1997), "Decay Characteristics of HIV-1-infected Compartments during Combination Therapy," Nature, 387, 188-191.
33. Perelson, A. S., and Nelson, P. W. (1999), "Mathematical Analysis of HlV-I Dynamics in Vivo," SIAM Reviews, 41, 3-44.
34. Pitt, M. K., and Shephard, N. (1999), "Filtering via Simulation: Auxiliary Particle Filters," Journal of the Amereri can Statistical Association, 94, 590-599.
35. Robinson, G.K. (1991), "That BLUP Is a Good Thing: The Estimation of Random Effects," Statistical Science, 6, 15-51.
36. Ruppert, D., Wand, M.P., and Carroll, R.J. (2003), Semiparametric Regression, New York: Cambridge University Press.
37. + T-cell Infection by HIV and Some Monte Carlo Studies," Mathematical Bioscience, 147, 173-205.
38. _ (2005), Deterministic and Stochastic Models of AIDS Epidemics and HIV Infections with Intervention, Singapore: World Scientific.
39. Wahba, G. (1978), "Improper Priors, Spline Smoothing and the Problem of Guarding against Model Errors in Regression," Journal of the Royal Statistical Society, Ser. B, 40, 364-372.
40. _ (1990), Spline Models for Observational Data, CBMS-NSF Regional Conference Series in Applied Mathematics, Vol. 59, Philadelphia: Society of Industrial and Applied Mathematics.
41. Wang, Y. (1998), "Smoothing Spline Models with Correlated Random Errors," Journal of the American Statistical Association, 93, 341-348.
42. Wecker, W. E., and Ansley, C. F. (1983), "The Signal Extraction Approach to Nonlinear Regression and Spline Smoothing," Journal of the American Statistical Association, 78, 81-89.
43. Wei, X., Ghosh, S. K., Taylor, M. E., et al. (1995), "Viral Dynamics in Human Immunodeficiency Virus Type 1 Infection," Nature, 373, 117-122.
44. West, M., and Harrison, J. (1997), Bayesian Forecasting and Dynamic Models, New York: Springer-Verlag.
45. Wu, C., and Chiang, C. (2000), "Kernel Smoothing on Varying Coefficient Models with Longitudinal Dependent Variables," Statistica Sinica, 10, 433-456.
46. Wu, H., and Ding, A. A. (1999), "Population HIV-1 Dynamics in Vivo: Applicable Models and Inferential Tools for Virological Data from AIDS Clinical Trials," Biometrics, 55, 410-418.