Inferring stochastic dynamics from functional data

Biometrika

Volumn 99, Issue 3, 2012, Pages 533-550

  Verzelen, Nicolas ^a   Tao, Wenwen ^b   Müller, Hans Georg ^b  

^a CEMAGREF   (France)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Empirical dynamic; Functional data analysis; Goodness of fit; Growth curve; Smoothing

Indexed keywords

EID: 84865457072     PISSN: 00063444     EISSN: 14643510     Source Type: Journal    
DOI: 10.1093/biomet/ass015     Document Type: Article

References (32)

1. BELLMAN, R.&ROTH, R. (1971). The use of splines with unknown end points in the identification of systems. J. Math. Anal. Appl. 34, 26-33.
2. BRUNEL, N. (2008). Parameter estimation of ODE's via nonparametric estimators. Electron. J. Statist. 2, 1242-67.
3. CHEN, J. & WU, H. (2008). Efficient local estimation for time-varying coefficients in deterministic dynamic models with applications to HIV-1 dynamics. Ann. Statist. 103, 369-84.
4. CHIANG, C., RICE, J. & WU, C. (2001). Smoothing spline estimation for varying coefficient models with repeatedly measured dependent variables. J. Am. Statist. Assoc. 96, 605-19.
5. ELLNER, S., SEIFU, Y.&SMITH, R. (2002). Fitting population dynamic models to time-series data by gradient matching. Ecology 83, 2256-70.
6. FAN, J. & GIJBELS, I. (1996). Local Polynomial Modelling and Its Applications. London: Chapman & Hall.
7. GASSER, T. & MÜLLER, H.-G. (1984). Estimating regression functions and their derivatives by the kernel method. Scand. J. Statist. 11, 171-85.
8. GASSER, T.,MÜLLER, H.-G., K̈OHLER, W.,MOLINARI, L. & PRADER, A. (1984). Nonparametric regression analysis of growth curves. Ann. Statist. 12, 210-29.
9. GOLUB, G., HEATH, M. & WAHBA, G. (1979). Generalized cross-validation as a method for choosing a good ridge parameter. Technometrics 21, 215-23.
10. HANSEN, B., CORTINA-BORJA, M. & RATCLIFFE, S. (2003). Assessing non-linear estimation procedures for human growth models. Ann. Hum. Biol. 30, 80-96.
11. HOFFMANN, M. (1999). Adaptive estimation in diffusion processes. Stoch. Proces. Appl. 79, 135-63.
12. HOLTE, S.,MELVIN, A.,MULLINS, J., TOBIN, N. & FRENKEL, L. (2006). Density-dependent decay in HIV-1 dynamics. J. Acq. Immun. Defic. Synd. 41, 266-76.
13. HOOKER, G. (2009). Forcing Function Diagnostics for Nonlinear Dynamics. Biometrics 65, 928-36.
14. JACOD, J. (2000). Non-parametric kernel estimation of the coefficient of a diffusion. Scand. J. Statist. 27, 83-96.
15. JONES, H. & BAYLEY, N. (1941). The Berkeley Growth Study. Child Dev. 12, 167-73.
16. JONES, M. C. & FOSTER, P. J. (1996). A simple nonnegative boundary correction method for kernel density estimation. Statist. Sinica 6, 1005-13.
17. LIANG, H. &WU, H. (2008). Parameter estimation for differential equation models using a framework of measurement error in regression models. J. Am. Statist. Assoc. 103, 1570-83.
18. MAS, A. & PUMO, B. (2009). Functional linear regression with derivatives. J. Nonparam. Statist. 21, 19-40.
19. MIAO, H., DYKES, C., DEMETER, L. M. & WU, H. (2009). Differential equation modeling of HIV viral fitness experiments: Model identification, model selection, and multimodel inference. Biometrics 65, 292-300.
20. MÜLLER, H.-G. (1987). Weighted local regression and kernel methods for nonparametric curve fitting. J. Am. Statist. Assoc. 82, 231-8.
21. MÜLLER, H.-G. (1991). Smooth optimum kernel estimators near endpoints. Biometrika 78, 521-30.
22. MÜLLER, H.-G. & YAO, F. (2010). Empirical dynamics for longitudinal data. Ann. Statist. 38, 3458-86.
23. PAUL, D., PENG, J. & BURMAN, P. (2011). Semiparametric modeling of autonomous nonlinear dynamical systems with applications. Ann. Appl. Statist. 5, 2078-108.
24. PERELSON, A., ESSUNGER, P., CAO, Y., VESANEN, M., HURLEY, A., SAKSELA, K., MARKOWITZ, M. & HO, D. (1997). Decay characteristics of HIV-l-infected compartments during combination therapy. Nature 387, 188-91.
25. PREECE, M. & BAINES, M. (1978). A new family of mathematical models describing the human growth curve. Ann. Hum. Biol. 5, 1-24.
26. RAMSAY, J. O. & SILVERMAN, B. W. (2005). Functional Data Analysis. New York: Springer, 2nd ed.
27. RAMSAY, J. O., HOOKER, G., CAMPBELL, D. & CAO, J. (2007). Parameter estimation for differential equations: a generalized smoothing approach. J. R. Statist. Soc. B 69, 741-96. With discussions and a reply by the authors.
28. REDDY, S. K. & DASS, M. (2006). Modeling on-line art auction dynamics using functional data analysis. Statist. Sci. 21, 179-93.
29. SCHIMEK, M., ed., 2000), Smoothing and Regression. New York: John Wiley.
30. SENT ÜRK, D. & MÜLLER, H.-G. (2010). Functional varying coefficient models for longitudinal data. J. Am. Statist. Assoc. 105, 1256-64.
31. TANNER, J., WHITEHOUSE, R. & TAKAISHI, M. (1966). Standards from birth to maturity for height, weight, height velocity, and weight velocity: British children. Arch. Dis. Child. 41, 613-35.
32. WANG, S., JANK, W., SHMUELI, G. & SMITH, P. (2008). Modeling price dynamics in eBay auctions using principal differential analysis. J. Am. Statist. Assoc. 103, 1100-18.