Empirical dynamics for longitudinal data

Annals of Statistics

Volumn 38, Issue 6, 2010, Pages 3458-3486

  Müller, Hans Georg ^a   Yao, Fang ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF TORONTO   (Canada)

Author keywords

Functional data analysis; Gaussian process; Longitudinal data; Stochastic differential equation

Indexed keywords

EID: 78650114165     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/09-AOS786     Document Type: Article

References (40)

1. ASH, R. B. and GARDNER, M. F. (1975). Topics in Stochastic Processes. Probability and Mathematical Statistics 27. Academic Press, New York. MR0448463
2. BAPNA, R., JANK, W. and SHMUELI, G. (2008). Price formation and its dynamics in online auctions. Decis. Support Syst. 44 641-656.
3. BOSQ, D. (2000). Linear Processes in Function Spaces: Theory and Applications. Springer, New York. MR1783138
4. DAUXOIS, J., POUSSE, A. and ROMAIN, Y. (1982). Asymptotic theory for the principal component analysis of a vector random function: Some applications to statistical inference. J. Multivariate Anal. 12 136-154. MR0650934
5. FAN, J. and GIJBELS, I. (1996). Local Polynomial Modelling and its Applications. Chapman and Hall, London. MR1383587
6. FINE, J. (1987). On the validity of the perturbation method in asymptotic theory. Statistics 18 401-414. MR0898411
7. GASSER, T. and MÜLLER, H.-G. (1984). Estimating regression functions and their derivatives by the kernel method. Scand. J. Statist. 11 171-185. MR0767241
8. GASSER, T., MÜLLER, H.-G., KÖHLER, W., MOLINARI, L. and PRADER, A. (1984). Nonparametric regression analysis of growth curves. Ann. Statist. 12 210-229. MR0733509
9. GERVINI, D. and GASSER, T. (2005). Nonparametric maximum likelihood estimation of the structural mean of a sample of curves. Biometrika 92 801-820. MR2234187
10. GRENANDER, U. (1950). Stochastic processes and statistical inference. Ark. Mat. 1 195-277. MR0039202
11. HALL, P. (1984). Integrated square error properties of kernel estimators of regression functions. Ann. Statist. 12 241-260. MR0733511
12. HALL, P., MÜLLER, H.-G. and WANG, J.-L. (2006). Properties of principal component methods for functional and longitudinal data analysis. Ann. Statist. 34 1493-1517. MR2278365
13. HÄRDLE, W. and GASSER, T. (1985). On robust kernel estimation of derivatives of regression functions. Scand. J. Statist. 12 233-240. MR0817941
14. JANK, W. and SHMUELI, G. (2005). Profiling price dynamics in online auctions using curve clustering. SSRN eLibrary. Working Paper RHS-06-004, Smith School of Business, Univ. Maryland.
15. JANK, W. and SHMUELI, G. (2006). Functional data analysis in electronic commerce research. Statist. Sci. 21 155-166. MR2324075
16. JONES, M. C. and RICE, J. A. (1992). Displaying the important features of large collections of similar curves. Amer. Statist. 46 140-145.
17. KATO, T. (1995). Perturbation Theory for Linear Operators. Springer, Berlin. MR1335452
18. KIRKPATRICK, M. and HECKMAN, N. (1989). A quantitative genetic model for growth, shape, reaction norms, and other infinite-dimensional characters. J. Math. Biol. 27 429-450. MR1009899
19. LIU, B. and MÜLLER, H.-G. (2008). Functional data analysis for sparse auction data. In Statistical Methods in eCommerce Research (W. Jank and G. Shmueli, eds.) 269-290. Wiley, New York. MR2414047
20. LIU, B. and MÜLLER, H.-G. (2009). Estimating derivatives for samples of sparsely observed functions, with application to on-line auction dynamics. J. Amer. Statist. Assoc. 104 704-714. MR2541589
21. MAS, A. and MENNETEAU, L. (2003). Perturbation approach applied to the asymptotic study of random operators. In High Dimensional Probability, III (Sandjberg, 2002). Progress in Probability 55 127-134. Birkhäuser, Basel. MR2033885
22. MAS, A. and PUMO, B. (2007). The ARHD model. J. Statist. Plann. Inference 137 538-553. MR2298956
23. MAS, A. and PUMO, B. (2009). Functional linear regression with derivatives. J. Nonparametr. Stat. 21 19-40. MR2483857
24. RAMSAY, J. (2000). Differential equation models for statistical functions. Canad. J. Statist. 28 225-240. MR1777224
25. RAMSAY, J. O., HOOKER, G., CAMPBELL, D. and CAO, J. (2007). Parameter estimation for differential equations: A generalized smoothing approach (with discussion). J. R. Stat. Soc. Ser. B Stat. Methodol. 69 741-796. MR2368570
26. RAMSAY, J. O. and SILVERMAN, B. W. (2005). Functional Data Analysis, 2nd ed. Springer, New York. MR2168993
27. REDDY, S. K. and DASS, M. (2006). Modeling on-line art auction dynamics using functional data analysis. Statist. Sci. 21 179-193. MR2324077
28. REITHINGER, F., JANK, W., TUTZ, G. and SHMUELI, G. (2008). Modelling price paths in on-line auctions: Smoothing sparse and unevenly sampled curves by using semiparametric mixed models. J. Roy. Statist. Soc. Ser. C 57 127-148. MR2420433
29. RICE, J. A. (2004). Functional and longitudinal data analysis: Perspectives on smoothing. Statist. Sinica 631-647. MR2087966
30. RICE, J. A. and WU, C. O. (2001). Nonparametric mixed effects models for unequally sampled noisy curves. Biometrics 57 253-259. MR1833314
31. SHI, M., WEISS, R. E. and TAYLOR, J. M. G. (1996). An analysis of paediatric CD4 counts for Acquired Immune Deficiency Syndrome using flexible random curves. J. Roy. Statist. Soc. Ser. C 45 151-163. (Pubitemid 126331741)
32. STANISWALIS, J. G. and LEE, J. J. (1998). Nonparametric regression analysis of longitudinal data. J. Amer. Statist. Assoc. 93 1403-1418. MR1666636
33. SY, J. P., TAYLOR, J. M. G. and CUMBERLAND, W. G. (1997). A stochastic model for the analysis of bivariate longitudinal AIDS data. Biometrics 53 542-555.
34. WANG, N., CARROLL, R. J. and LIN, X. (2005). Efficient semiparametric marginal estimation for longitudinal/clustered data. J. Amer. Statist. Assoc. 100 147-157. MR2156825
35. WANG, L., LI, H. and HUANG, J. Z. (2008). Variable selection in nonparametric varyingcoefficient models for analysis of repeated measurements. J. Amer. Statist. Assoc. 103 1556-1569. MR2504204
36. WANG, S., JANK, W., SHMUELI, G. and SMITH, P. (2008). Modeling price dynamics in ebay auctions using principal differential analysis. J. Amer. Statist. Assoc. 103 1100-1118.
37. YAO, F. and LEE, T. C. M. (2006). Penalized spline models for functional principal component analysis. J. R. Stat. Soc. Ser. B Stat. Methodol. 68 3-25. MR2212572
38. YAO, F., MÜLLER, H.-G. and WANG, J.-L. (2005). Functional data analysis for sparse longitudinal data. J. Amer. Statist. Assoc. 100 577-590. MR2160561 (Pubitemid 40816595)
39. ZHAO, X., MARRON, J. S. and WELLS, M. T. (2004). The functional data analysis view of longitudinal data. Statist. Sinica 14 789-808. MR2087973
40. ZIEMER, W. (1989). Weakly Differentiable Functions: Sobolev Spaces and Functions of Bounded Variation. Springer, New York. MR1014685