Nonparametric estimation of correlation functions in longitudinal and spatial data, with application to colon carcinogenesis experiments

Annals of Statistics

Volumn 35, Issue 4, 2007, Pages 1608-1643

  Li, Yehua ^a   Wang, Naisyin ^b   Hong, Meeyoung ^b   Turner, Nancy D ^b   Lupton, Joanne R ^b   Carroll, Raymond J ^b  

^a UNIVERSITY OF GEORGIA   (United States)

^b TEXAS A AND M UNIVERSITY   (United States)

Author keywords

Asymptotic theory; Bootstrap; Colon carcinogenesis; Correlation functions; Dependent data; Functional data; Gene expression; Kernel regression; Nonparametric regression; Spatial data; Time series

Indexed keywords

EID: 50449084238     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/009053607000000082     Document Type: Article

References (18)

1. BESAG, J. and HIGDON, D. (1999). Baysian analysis of agricultural field experiments (with discussion). J. R. Stat. Soc. Ser. B Stat. Methodol. 61 691-746.
2. BESAG, J., YORK, J. and MOLLIÉ, A. (1991). Baysian image restoration, with two applications in spatial statistics (with discussion). Ann. Inst. Statist. Math. 43 1-59.
3. CRESSIE, N. A. C. (1993). Statistics for Spatial Data. Wiley, New York.
4. CRESSIE, N. A. C. and HUANG, H.-C. (1999). Classes of nonseparable, spatio-temporal stationary covariance functions. J. Amer. Statist. Assoc. 94 1330-1340.
5. DIGGLE, P. and VERBYLA, A. P. (1998). Nonparametric estimation of covariance structure in longitudinal data. Biometrics 54 401-415.
6. GUAN, Y., SHERMAN, M. and CALVIN, J. A. (2004). A nonparametric test for spatial isotropy using subsampling. J. Amer. Statist. Assoc. 99 810-821.
7. HALL, P., FISHER, N. I. and HOFFMANN, B. (1994). On the nonparametric estimation of covariance functions. Ann. Statist. 22 2115-2134.
8. HALL, P. and PATIL, P. (1994). Properties of nonparametric estimators of autocovariance for stationary random fields. Probab. Theory Related Fields 99 399-424.
9. IBRAGIMOV, I. A. and LINNIK, Y. V. (1971). Independent and Stationary Sequences of Random Variables. Wolters-Noordhoff, Groningen.
10. KARR, A. F. (1986). Inference for stationary random fields given Poisson samples. Adv. in Appl. Probab. 18 406-422.
11. MORRIS, J. S., WANG, N., LUPTON, J. R., CHAPKIN, R. S., TURNER, N. D., HONG, M. Y. and CARROLL, R. J. (2001). Parametric and nonparametric methods for understanding the relationship between carcinogen-induced DNA adduct levels in distal and proximal regions of the colon. J. Amer. Statist. Assoc. 96 816-826.
12. POLITIS, D. N. and SHERMAN, M. (2001). Moment estimation for statistics from marked point processes. J. R. Stat. Soc. Ser. B Stat. Methodol. 63 261-275.
13. RAMSAY, J. O. and SILVERMAN, B. W. (1997). Functional Data Analysis. Springer, New York.
14. SERFLING, R. J. (1980). Approximation Theorems of Mathematical Statistics. Wiley, New York.
15. SHAO, J. and TU, D. (1995). The Jackknife and Bootstrap. Springer, New York.
16. STEIN, M. L. (1999). Interpolation of Spatial Data: Some Theory for Kriging. Springer, New York.
17. STEIN, M. L. (2005). Space-time covariance functions. J. Amer. Statist. Assoc. 100 310-321.
18. YAO, F., MÜLLER, H.-G. and WANG, J.-L. (2005). Functional data analysis for sparse longitudinal data. J. Amer. Statist. Assoc. 100 577-590.